1797, "crape-like fabric," especially white or colored, not the ordinary black for mourning, from French crêpe, Old French crespe "ruff, ruffle, frill" (14c.), from Latin crispa, fem. of crispus "curled, wrinkled, having curly hair," from PIE root *sker- (2) "to turn, bend." Crepe paper is attested by 1895.
Meaning "small, thin pancake" is from 1877, from French galette crêpe "curled/wrinkled pancake" (compare crumpet). Recipes for what seem to be similar things are in English cookery books from late 14c., often as crispes, cryspes, but at least once as cryppys. Related: Creperie. Crepe suzette "light pancake served rolled or folded, sprinkled with orange liqueur or brandy and flambéed," is by 1910 in English (suzette pancake is from 1907) and was the usual form until c. 1980.
Contemporary evidence suggests that its most likely creator was a head waiter at Restaurant Paillard in Paris in 1889, and that it was named in honour of an actress in the Comédie Française who played the part of a maid serving pancakes. ... [T]hey were for perhaps the first two thirds of the twentieth century the epitome of the luxurious, expensive, and exclusive dessert. [Ayto, "Diner's Dictionary"]