late 13c., anhaunsen "to raise, make higher," from Anglo-French enhauncer, probably from Old French enhaucier "make greater, make higher or louder; fatten, foster; raise in esteem," from Vulgar Latin *inaltiare, from Late Latin inaltare "raise, exalt," from altare "make high," from altus "high," literally "grown tall" (from PIE root *al- (2) "to grow, nourish"). The meaning "raise in station, wealth, or fame" attested in English from c. 1300. Related: Enhanced; enhancing.
The -h- in Old French supposedly is from influence of Frankish *hoh "high." The -n- perhaps is due to association with Provençal enansar, enanzar "promote, further," from enant "before, rather," from Latin in + ante "before."