2 English words descend from French bouffant, most common first.
bouffantOf hair or clothing, full-bodied or puffy; puffed out away from head or body.
buffontAn item of neckwear (a neckerchief), usually of linen, gauze, or lace, worn around the neck and puffed out over the bosom, popular from the 1750s to 1790s.