English word fae comes from Vulgar Latin Fata, Latin fata, and later Latin *Fata ((Vulgar Latin) one of the Fates, a goddess of fate.)
Fata (Vulgar Latin)
fata (Latin)
*Fata (Latin)
(Vulgar Latin) one of the Fates, a goddess of fate.
fae (Old French)
fee (Middle French)
fei (Middle English)
fae (English)
(etymology 2) (etymology 3).