C17: from French, literally: a sweet letter, from billet (see billet1) + doux sweet, from Latin dulcis
Word Origin and History for billet-doux
n.
also billet doux, 1670s, "love letter," French, literally "sweet note," from billet "document, note" (14c., diminutive of bille; see bill (n.1)) + doux "sweet," from Latin dulcis (see dulcet).