Enhance
Middle English (formerly also as inhance ): from Anglo-Norman French enhauncer, based on Latin in- (expressing intensive force) + altus ‘high’. The word originally meant ‘elevate’ (literally and figuratively), later ‘exaggerate, make appear greater’, also ‘raise the value or price of something’. Current senses date from the early 16th century.
wiktionary
From Middle English enhauncen, from Anglo-Norman enhauncer, from Old French enhaucier(“make greater”), from Late Latin inaltare(“exalt”), from Latin in + altus(“high”).
etymonline
enhance (v.)
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." 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."