The name Apache designates primarily a member of a North-American people living chiefly in New Mexico and Arizona.

This is the origin of the name Apache, according to Handbook of American Indians North of Mexico (Washington, D.C.: Government Printing Office, 1907), edited by Frederick Webb Hodge (1864-1956):

Apache (probably from ápachu, ‘enemy,’ the Zuñi name for the Navaho, who were designated “Apaches de Nabaju” by the early Spaniards in New Mexico). […] The Apache call themselves N’de, Dĭnë, Tĭnde, or Inde, ‘people.’

This, incidentally, illustrates the fact that the name a particular nation, community or ethnic group gives itself is generally flattering or, at least, neutral, whereas the name it is given by an external people is often derogatory.
—Another example: According to Handbook of American Indians North of Mexico, Dakota (the self-designation of a North-American people) means allies, whereas Sioux (another name for the Dakota people) derives from “Chippewa Nadowe-is-iw, a diminutive of nadowe, ‘an adder,’ hence ‘an enemy.’”

At the turn of the 20^th century, by association with the reputed ferocity of the North-American Indian people, Apache came to designate a violent street ruffian in Paris.

This depiction of an Apache is from Le Petit Journal (Paris, France) of Sunday 20^th October 1907:

 

The following article, published in La Charente (Angoulême, France) of Friday 6^th July 1900, gives an account of the ruffians’ gruesome ways—the translation is followed by the original French article:

THE BELLEVILLE SAVAGES

For some time, dangerous prowlers, known in the world of the escarps under the name of the “Apaches”, have been spreading terror on the outer boulevards and chiefly on the boulevard of Belleville which they systematically bleed as soon as the sun sets.
Several of those criminals, recognisable by the wide black belt that they wear round the waist, were captured by Mr Girard, police superintendent. Unfortunately a certain number of them have so far managed to escape the policemen launched on their tail and they have continued, without respite, with the string of their sinister exploits.
A button-maker, Mr Julien Meunier, aged thirty-seven, living rue des Amandiers, was the victim, during the night of Thursday to Friday, of those bandits who do evil for no reason, simply for the sake of doing it.
Mr Meunier, after spending the evening at friends’, was peacefully going back home, around half past one in the morning, when in front of the nᵒ 132 of the boulevard de Belleville, he was suddenly surrounded by four individuals, armed with bludgeons and daggers.
— Follow us and be quiet!… said to him a tall fellow who seemed to be the gang leader.
Terrorised, Mr Meunier obeyed without a murmur this categorical order, given moreover in a tone of voice which brooked no reply.
The attackers took him into a dark street of which he could not read the name; then, in the same authoritative tone, the leader ordered him to sit down.
The scene that then took place is horrific and, indeed, as for refinement of cruelty, real Apaches would not have found better.
Be the judges: When the patient had sat down, one of the bandits took from his pocket a bottle of absinth and forced him to drink straight from it. Every time he stopped, the leader delivered a tremendous kick to the small of his back to force him to carry on.
Soon blind drunk, Mr Meunier dropped the flask which shattered on the cobbles.
At the break of day, workmen on their way to work found, lying in a pool of blood, the poor man completely disfigured.
His right eye was out of the eye socket and was hanging on the cheek; with a knife blow, the scoundrels had also severed the nose, and finally, to complete their sanguinary exploits, they had slit the left cheek with a dagger blow. The weapon was still in the wound and the blade was coming out of the mouth.
Before leaving the assassins had stuck on the tip of the blade a sheet of paper, torn out of a notebook, on which one could read, despite the blood that covered it, these words written with a pencil: “The Apaches”.
Mr Meunier was taken to Saint-Louis hospital in a state that leaves little hope of his being saved.
An investigation was immediately opened by Mr Girard, police superintendent of Belleville, and the Criminal Investigation Department has launched at once its best policemen in search of the cruel bandits.

Original text:

LES SAUVAGES DE BELLEVILLE

Depuis quelque temps, de dangereux rôdeurs, connus dans le monde des escarpes sous le nom des « Apaches », répandent la terreur sur les boulevards extérieurs et principalement sur le boulevard de Belleville qu’ils mettent en coupe réglée dès la chute du jour.
Plusieurs de ces malfaiteurs, reconnaissables à une ample ceinture noire qu’ils porte [sic] autour de la taille, ont été capturés par M. Girard, commissaire de police. Malheureusement un certain nombre d’entre eux ont réussi jusqu’ici à échapper aux agents lancés à leurs trousses et ils continuent, sans répit, la série de leurs sinistres exploits.
Un ouvrier boutonnier, M. Julien Meunier, âgé de trente-sept ans, demeurant rue des Amandiers, a été victime, pendant la nuit de jeudi à vendredi, de ces malandrins qui font le mal sans raison, simplement pour le plaisir de le faire.
M. Meunier, après avoir passé la soirée chez des amis, regagnait tranquillement son domicile, vers une heure et demie du matin, lorsqu’en face du nᵒ 132 du boulevard de Belleville, il fut soudain entouré par quatre individus, armés de casse-tête et de poignards.
— Suis-nous et tais-toi !… lui dit un grand gaillard qui semblait être le chef de la bande.
Terrorisé, M. Meunier obéit sans murmurer à cet ordre formel, donné d’ailleurs sur un ton qui n’admettait pas de réplique.
Les agresseurs l’entraînèrent dans une rue obscure dont il ne put lire le nom ; puis, du même ton d’autorité, le chef lui ordonna de s’asseoir.
La scène qui se passa alors est épouvantable et, certes, comme raffinement de cruauté, de véritables Apaches n’eussent pas trouvé mieux.
Qu’on en juge : Lorsque le patient se fut assis, l’un des bandits sortit de sa poche une bouteille d’absinthe et le força à boire au goulot. Chaque fois qu’il s’arrêtait, le chef lui décochait dans les reins un formidable coup de pied pour le forcer à continuer.
Bientôt ivre-mort, M. Meunier laissa échapper la fiole qui se brisa sur le pavé.
Au point du jour, des ouvriers se rendant à leur travail trouvèrent, baignant dans une mare de sang, le malheureux complètement défiguré.
Son œil droit était sorti de l’orbite et pendait sur la joue ; d’un coup de couteau, les misérables lui avaient également tranché le nez, et enfin, pour compléter leurs exploits sanguinaires, ils lui avaient fendu la joue gauche d’un coup de poignard. L’arme était restée dans la plaie et la lame ressortait par la bouche.
Avant de se retirer les assassins avaient fiché au bout de la lame une feuille de papier, arrachée à un carnet de poche, sur laquelle on put lire, malgré le sang dont elle était maculée, ces mots tracés au crayon : « Les Apaches ».
M. Meunier a été transporté à l’hôpital Saint-Louis dans un état qui laisse peu d’espoir de le sauver.
Une enquête a été immédiatement ouverte par M. Girard, commissaire de police de Belleville, et le service de la sûreté a lancé aussitôt ses meilleurs agents à la recherche des cruels bandits.

The following article was published in The Porter Enterprise (Porter, Oklahoma) of Friday 4^th June 1900—Casque d’Or was Amélie Élie (1878-1933):

“LES APACHES” of PARIS
By Edward W. Pickard

One morning not long ago a well-dressed foreigner, evidently an American tourist, was found dead on the pavement in a side street of Paris. Twisted about his neck was a dirty handkerchief with which he had been strangled; he had been brutally kicked and beaten, and in his chest were several knife wounds, any one of which would have killed him. The unfortunate man had been stripped of all money, jewelry and other valuables.
“Les Apaches,” said the police, stolidly. “He should have known better than to go prowling about alone at night.” And in the police records another murder was put on the score of the thugs of the “gay capital.”
Paris is not proud of her Apaches, and the rest of the world has known little of these criminal bands, though theater-goers in many American cities during the last season were given a glimpse of one phase of their life in the skillful but revolting “Apache dance” imported from the French music halls. Yet the story of the origin, development and deeds of these outlaw gangs is fascinating, if not edifying.
Nearly ten years ago there appeared suddenly in the underworld of Paris a young woman so beautiful and animated that she at once attracted general attention and admiration among its other denizens. Her head was crowned with a great mass of lovely reddish-gold hair, on account of which she was promptly nicknamed “Casque d’Or,” or “Golden Helmet.” Suitors quickly flocked about the girl and in time she selected from among them as her protector one Lecat, known among his comrades as a clever thief and a bold fighter whom the police would be glad to have behind the bars.
All went well for a time, until there came on the scene a more attractive scoundrel, named Manda. Pretty, fickle Golden Helmet promptly transferred her affections to the newcomer, and then the trouble began. Lecat, the forsaken, vowed vengeance on his successful rival and summoned his followers to his aid. Manda also had no lack of friends, and soon all the thugs in the district of the Halles or markets had ranged themselves on one side or the other. Many a bloody battle was fought in the streets between the two bands, cheered on by their female friends, and not a few men were slain in these conflicts. Finally in one of the fiercest of the encounters Lecat himself was killed, and Golden Helmet shouted aloud in joy. But her triumph was short-lived. Another leader for Lecat’s band, known as “Le Manchot,” sprang up and the feud was continued with increased fury. One night Le Manchot caught Manda off his guard and plunged a knife deep into his back, and for weeks the stricken leader lay in hospital near to death. He recovered at last and was being taken in an ambulance to a cell when the bloodthirsty Le Manchot, seeing his victim escaping from his vengeance, broke through the police guard, leaped into the vehicle and stabbed Manda to death. For this murder Le Manchot is now serving a life sentence.
Golden Helmet, made notorious by the succession of battles and crimes which her attractions had instigated, now sought other conquests, and decided that the drama was her forte. Only the intervention of the police prevented her exploitation by an unscrupulous variety hall manager.
Golden Helmet then speedily sank out of sight, but the rivalry for her favor had lasting results.
Always the Apaches have one “queen” whose rule over them is absolute if temporary. One of the most notorious of these was “Chiffonnette,” who reigned last year. She was 23 years old, tall and graceful, and would have been a beauty save for the loss of one eye and the presence of many scars, the results of her numerous boulevard battles. She was elaborately tattooed and was mighty proud of that adornment. Chiffonnette’s career came to an untimely end last New Year’s day, when she engaged in a desperate fight with another woman whom she hated. Cheered on by a crowd of her male and female subjects, the queen finally stabbed her antagonist to death with a stiletto, and now she is a prisoner in St. Lazare.
This year’s queen of the Apaches is Pepe. She is only 18 years old and as pretty as a picture, but as fierce as a tigress and a fit leader for the wretches by whom she is adored.
The comparative immunity from arrest and punishment enjoyed by the Apaches is due to their really wonderful organization. They form a community by themselves, apart from all the rest of Paris, with their own laws, courts and executioners; their secret passwords, and almost their own language, for the argot they use is practically unintelligible to others. Merciless toward their victims, they are no less merciless in punishing those of their own number who are convicted of treachery.
A few years ago one Painblanc was accused of being in league with the police. He was formally brought to trial, the judge being a leader known as “l’Espagnol.” The charge against Painblanc was not fully proved, but his loyalty was so doubtful that he was sentenced to exile. Rising from his chair in the obscure dive where the trial was being held, he hurled his knife at l’Espagnol with unerring accuracy, and the judge fell dead with the blade in his heart. The police rushed in and carried Painblanc to prison, the Apaches making no effort to save him.
Another alleged traitor was Albert Durin. He was condemned to death and two Apaches tied him to the rails of a tunnel of the Belt Line railway of Paris. He was found before a train passed and rescued. How many traitors have been executed by their comrades it is impossible to know, for only in such cases as the foregoing do the police learn about the operations of the “tribunals.”
The Apache highwayman operates swiftly and skillfully, and lone strangers in the streets of Paris are never safe from his attacks. His favorite method, known as “le coup du Pere Francois,” is to strangle his victim by twisting a handkerchief about his neck. After robbing the senseless man, the thug frequently will kill him with the knife, for the Apaches seem to delight in wanton murder done in what they choose to consider an “artistic” way. If the criminal is arrested, a score of his companions spring up apparently from the very pavement, and unless the police are in force they are speedily routed and the prisoner is rescued.
An observant visitor in Paris may see Apaches, male and female, on almost any street, but it is in the Place de la Roquette that they are to be found in crowds on ocasion [sic]. There is set up the recently restored guillotine, and whenever there is to be an execution the Apaches flock from all districts of the city to witness the ghastly sight. Silently they stand, gazing at the grim instrument of death, until the condemned individual is brought forth. Then jeers and howls break forth from the crowd, and as the knife falls the Apaches rush forward to dip their handkerchiefs in the blood. These they preserve as souvenirs, or sell them to the degenerates of the upper classes.
Strangely enough, the male Apaches nearly all look alike. They are hollow-cheeked, dark-haired, furtive-eyed, shambling of gait and sallow of complexion—always easily recognized among the throngs on the streets. The women on the other hand, as a rule, are handsome, spirited and intelligent. They dress well and give especial attention to the care of their hair, which they never cover with a hat. All of them, men and women, profess to follow some trade as a safeguard against the occasional raids of the police on their haunts.
Official Paris is somewhat dismayed by the rapidly growing menace of these Apaches bands. The number of robberies and murders attributable to them is increasing monthly, and as the victims very often are travelers from foreign lands, the crimes are having an appreciable effect on tourist business.