The name Indian summer denotes a period of unusually calm dry warm weather, often accompanied by a hazy atmosphere, occurring in late autumn in the northern United States and Canada. It is first recorded in an essay dated 1774 by its author, a Frenchman named Michel-Guillaume Jean de Crèvecœur (1735-1813).

As I have explained in origin of ‘Indian summer’ and French été sauvage’, this new name reflected the fact that to the Europeans living in the New World, these periods of unusually dry, warm weather were a newly-discovered local phenomenon.

But similar phenomena were already known in the Old World by various names.

In Tableau du climat et du sol des Etats-Unis d’Amérique (Paris, 1803), Constantin François de Chassebœuf (1757-1820), comte de Volney, likened both French l’été sauvage and English Indian summer to French l’été de la Saint-Martin:

Vers novembre, reparaît une série de beaux jours, appelés l’été sauvage (Indian-summer) : c’est ce que nous appelons en France l’été de la Saint-Martin ; mais il est devenu si rare et si court, que nous n’en parlons plus que par tradition.

In the translation of C. F. de Chassebœuf’s book, View of the Climate and Soil of the United States of America (London, 1804), Charles Brockden Brown (1771-1810) used Indian summer only, not l’été sauvage, and equated St. Martin’s Summer to All-Hallown Summer:

Towards November a succession of fine days appears, which are styled the Indian summer. This is what is called in France a St. Martin’s summer*; but it is here [= in France] grown so rare, and so short, that it is now spoken of only traditionally.
[translator’s note:] * In England, an All-hallown summer.

Both French l’été de la Saint-Martin and English St Martin’s summer designate a period of fine, mild weather around 11^th November, the feast day of St Martin of Tours. In The First part of King Henry the Sixth (around 1591), by the English poet and playwright William Shakespeare (1564-1616), Joan la Pucelle says:

(Folio 1, 1623)
This night the Siege assuredly Ile rayse:
Expect Saint Martins Summer, Halcyons dayes,
Since I haue entred into these Warres.

Similarly, St Luke’s (little) summer, or little summer of St Luke, is a period of fine dry weather around 18^th October, the feast day of St Luke the Evangelist. In Circle of the Seasons, and perpetual key to the calendar and almanack (London, 1828), Thomas Ignatius M. Forster wrote, about Luke Tide, from 11^th to 23^rd October:

The weather is often fine at this time of year. After it is gone we may expect the cold and fog of Allhallow Tide.
[…]
We have already said that fair, warm, and dry weather, often occurs about this time, and is called St. Luke’s Little Summer. A gentle breeze from the south, the thermometer about 60°, fair sky, and sunderclouds and other mixed clouds, with the sun slowly breaking out into full radiance, and the ground gradually drying, constitute the weather of this last act of summer, named after St. Luke.

In The First part of King Henry the Fourth (around 1597), Shakespeare makes Prince Henry use All-Hallown Summer to address Falstaff, seen as an older person who retains a youthful demeanour:

(Folio 1, 1623)
– Falstaff: Farwell, you shall finde me in Eastcheape.
– Prince Henry: Farwell the latter Spring. Farewell Alhollown Summer.