early 15c., from Old French ambre gris "gray amber," "a wax-like substance of ashy colour, found floating in tropical seas, a morbid secretion from the intestines of the sperm-whale. Used in perfumery, and formerly in cookery" [OED], via Medieval Latin from Arabic 'anbar (see amber). Its origin was known to Constantinus Africanus (obit c. 1087), but it was a mystery in Johnson's day, and he records nine different theories; "What sort of thing is Ambergrease?" was a type of a puzzling question beyond conjecture. King Charles II's favorite dish was said to be eggs and ambergris [Macauley, "History of England"].
Praise is like ambergris; a little whiff of it, by snatches, is very agreeable; but when a man holds a whole lump of it to his nose, it is a stink and strikes you down. [Pope, c. 1720]
French gris is from Frankish *gris or some other Germanic source (cognates: Dutch grijs, Old High German gris; see gray (adj.)).