Usually preceded by the definite article, the phrase eternal triangle designates a love-relationship in which one member of a married couple is involved with a third party.

This phrase is a loan translation from French triangle éternel, coined by the French author Alexandre Dumas fils (1824-1895) in L’Homme-Femme. Réponse à M. Henri d’Ideville (Paris: Michel Lévy Frères, Éditeurs, 1872)—cf., below, quotation 1 from Black & White (London, England) of 25^th August 1894.

However, in his pamphlet, Alexandre Dumas fils did not use the phrase triangle éternel in the sense of a love-relationship in which one member of a married couple is involved with a third party—the following is from page 25 of L’Homme-Femme:

Dieu, l’homme et la femme, principes du monde, subsistent toujours les mêmes. Les trois côtés du triangle éternel sont donc représentés par Dieu, l’homme et la femme.
     translation:
God, man and woman, principles of the world, subsist always the same. The three sides of the eternal triangle are therefore represented by God, man and woman.

The use of the English phrase eternal triangle in the sense of a love-relationship in which one member of a married couple is involved with a third party seems to be the result of a misunderstanding: Alexandre Dumas fils did not use triangle éternel in this sense, but his pamphlet was about a wronged husband’s right to take the life of his adulterous wife. The following explanations are from Relaunching the Republican Campaign for Women’s Rights, Chapter 1 (pp. 15-52) of Debating the Woman Question in the French Third Republic, 1870–1920 (Cambridge University Press, 2017), by Karen Offen, Stanford University, California:

In the spring of 1872 a certain Arthur Leroy Du Bourg had murdered his wife and her lover (who happened to have been her husband’s best friend). Had Du Bourg murdered her under his own roof, he would not have been prosecuted, according to Article 324 of the French Penal Code. As this was not the case, Du Bourg was taken to court and tried for murder; he was convicted, but got off with a sentence of five years in prison.
In the French Penal Code, a man convicted for keeping a concubine under the same roof as his wife was subject only to a stiff fine; if he kept the concubine next door—or across the street—the man could not be prosecuted. What was more, a husband who discovered his wife in flagrante delicto in their common home and killed her would not be brought to justice; he was within his “right.” If he killed her under the roof of another man, he would be tried but more than likely would be acquitted (as several other men had been in recent months). By contrast, a wife who committed an act of vengeance against an unfaithful husband would be dealt with severely by the courts. A woman convicted of adultery could be imprisoned; not so the man.
Thus, the sensational trial of Monsieur Du Bourg, and the French public’s amazement that he was actually convicted, brought to the surface many entangled issues about morals and punitive laws. It generated a new outburst of debate on the woman question, focused on the double standard of sexual morality. […]
[…]
A lengthy and heated debate in print ensued between feminists, male and female, and those who upheld Du Bourg’s right to take the life of his adulterous wife. Henry d’Ideville, a friend of Dumas fils, first engaged the debate, arguing in Le Soir (15 May 1872) that the adulterous wife should be exonerated and divorce reestablished. He also critiqued the sexual double standard that allowed men free range before marriage, yet expected brides to be pure and sexually uninformed, and condemned unsuitable arranged marriages. Dumas fils then responded to d’Ideville in mid-July with L’Homme-femme, a rambling handbook of lacerating misogyny (but also not particularly complimentary to men), which he ended by invoking a wronged husband to defend his honor by killing an unfaithful wife: “TUE-LA!” [i.e., “KILL HER!”]

—Cf. also Why the French language is intrinsically sexist.

The earliest occurrences that I have found of the English phrase eternal triangle—used in the sense of a love-relationship in which one member of a married couple is involved with a third party—are as follows, in chronological order:

1-: From a review of Lord Ormont and His Aminta (London: Chapman and Hall, 1894), by the British novelist and poet George Meredith (1828-1909)—review published in Black & White (London, England) of Saturday 25^th August 1894 [Vol. 8, No. 186, page 239, column 1]:

His [i.e., George Meredith’s] story is simple in construction, however complex in style. It is concerned with the eternal triangle of Dumas: husband, wife and lover; but the finale rivals even Dumas in audacity of theory and plainness of issue.

2-: From The Stage, published in The Detroit Free Press (Detroit, Michigan, USA) of Sunday 15^th September 1895 [Vol. 60, No. 356, page 15, column 4]:

The title of Edwin Milton Royle’s play, “One Plus One Equals Three,” makes the tone of the drama easy to guess at, especially as it is called “a purpose play.” It is evidently on the idea that the French entertain—that marriage means the eternal triangle.

3-: From Stage Whispers, published in The Umpire (Manchester, Lancashire, England) of Sunday 19^th September 1897 [No. 708, page 3, column 1]:

The apogee of the Maudlin has at last been reached.
The plot of “The Wife of Scarli”—by the way, “Scarli’s Wife” is no relation to, nor half as entertaining as, “Scarli’s Aunt,”—done by Miss Nethersole on Friday night, is thin to attenuation, and cheap enough for a third-rate “domestic” drama.
The tune of the piece is played upon the eternal triangle, the Trusting Husband, the False Friend, and the Deceitful Wife.

4-: From The Argus (Melbourne, Victoria, Australia) of Saturday 22^nd January 1898 [No. 16,086, page 9, column 5]:

DOMESTIC TRAGEDY.
ATTEMPTED MURDER AND SUICIDE.
A HUSBAND SHOOTS HIS WIFE.
ALLEGED INFIDELITY.

“The eternal triangle of man, wife, and wife’s friend” has been again brought before the Melbourne public by the tragedy which took place about 11 o’clock last night in Goetz-lane, off Little Collins-street east.

5-: From The Stage, published in The Detroit Free Press (Detroit, Michigan, USA) of Tuesday 6^th February 1900 [Vol. 65, No. 135, page 4, column 4]:

The present status of what is known in theatrical circles as the Blair Independent movement is set forth by the Criterion as follows:
A little later in the season a very remarkable play by one of the German dramatists, Max Dreyer, will be given a hearing. In his comedy-drama entitled “Drei” (Three) he has treated the old fascinating subject of platonic affection—or, as we now call it, love in friendship—brightly, truthfully and, above all, logically. What may seem even more remarkable to those of us who remember what French playwrights almost invariably make of the eternal stage triangle, formed by the husband, the wife and “the other person,” he has handled his theme purely. Tears and smiles are skillfully mingled in “Drei,” and all the characters, however erratically they may behave, retain our sympathy.

6-: From a theatrical review, published in The St James’s Gazette (London, England) of Friday 11^th May 1900 [Vol. 11, No. 6,180, page 5, column 2]:

“A Patched-up Affair,” by Florence Warden, is an interesting and well-constructed piece with a strong dramatic situation. It presents what the French call “the eternal triangle” of husband, wife, and lover. But the treatment is anything but French; it is as wholesome as it is arresting. The principal parts were admirably played by Mr. George Alexander and Miss Fay Davis. Mr. Alexander exhibited to perfection the strong emotion of the Englishman who at the most strenuous moment is most calm, and is never betrayed into the ranting heroics of the Frenchman.

7-: From a theatrical review, published in The Gentlewoman. The Illustrated Weekly Journal for Gentlewomen (London, England) of Saturday 15^th September 1900 [Vol. 21, No. 532, page 340, column 3]:

“A Debt of Honour” at the St. James’s.
In his latest play, “A Debt of Honour,” Mr. Sydney Grundy goes from the A to Z of his dramatic alphabet. His play is interesting, deeply interesting up to a certain point, but he has no new solution to offer concerning the eternal triangle—two women and one man. He enlists all your sympathies for the loyal-hearted woman taken to wife by George Carylon, Q.C. He enlists all your sympathies for the woman who was his wife by the dictates of her heart, the woman who loved him truly and well for ten long years. By an adroit manipulation of his pieces Mr. Grundy brings these two women together.

8-: From Fashion Letters from a Fashionable Woman, by ‘Juno’, published in The Gentlewoman. The Illustrated Weekly Journal for Gentlewomen (London, England) of Saturday 6^th October 1900 [Vol. 21, No. 535, page 443, column 1]:

The theatres are all waking up and offering fresh fare. Just imagine Mr. Barrie writing a problem play. We went to it last night, “The Wedding Guest” at the Garrick. There is, of course the eternal triangle of two women and one man. It is harrowing rather, as the successive emotions of these three vary and complicate the situation. Miss Violet Vanbrugh is the “other” woman, Miss Dorothea Baird is the young girl wife, and Mr. H. B. Irving the bone of contention.