1530s, "fumes from a burning substance," from French parfum (16c.), from parfumer "to scent," from Old Provençal perfumar or cognate words in dialectal Italian (perfumare) or Spanish (perfumar), from Latin per "through" (from PIE root *per- (1) "forward," hence "through") + fumare "to smoke" (see fume (n.)). Meaning "substance containing agreeable essences of flowers, etc.," is attested from 1540s.
1530s, "to fill with smoke or vapor," from perfume (n.) or from French parfumer. Meaning "to impart a sweet scent to" is from 1530s. Related: Perfumed; perfuming.