mid-15c., "showy, finely dressed; gay, merry," from Old French galant "courteous," earlier "amusing, entertaining; lively, bold" (14c.), present participle of galer "rejoice, make merry," which is of uncertain origin. Perhaps from a Latinized verb formed from Frankish *wala- "good, well," from Proto-Germanic *wal- (source also of Old High German wallon "to wander, go on a pilgrimage"), from PIE root *wel- (2) "to wish, will" (see will (v.)), "but the transition of sense offers difficulties that are not fully cleared up" [OED]. Sense of "politely attentive to women" was adopted early 17c. from French. Attempts to distinguish this sense by accent are an 18c. artifice.
mid-15c., "man of fashion and pleasure," earlier "dissolute man, rake" (early 15c.); from gallant (adj.). As "one who is particularly attentive to women" probably by late 15c.