abandon (v.) Look up abandon at Dictionary.com
late 14c., "to give up (something) absolutely, relinquish control, give over utterly;" also reflexively, "surrender (oneself), yield (oneself) utterly" (to religion, fornication, etc.), from Old French abandoner "surrender, release; give freely, permit," also reflexive, "devote (oneself)" (12c.).

The Old French word was formed from the adverbial phrase à bandon "at will, at discretion," from à "at, to" (from Latin ad-; see ad-) + bandon "power, jurisdiction," from Latin bannum, "proclamation," which is from a Frankish or other Germanic word, from Proto-Germanic *bannan- "proclaim, summon, outlaw" (things all done by proclamation); see ban (v.).
Mettre sa forest à bandon was a feudal law phrase in the 13th cent. = mettre sa forêt à permission, i.e. to open it freely to any one for pasture or to cut wood in; hence the later sense of giving up one's rights for a time, letting go, leaving, abandoning. [Auguste Brachet, "An Etymological Dictionary of the French Language," transl. G.W. Kitchin, Oxford, 1878]
Meaning "to leave, desert, forsake (someone or something) in need" is from late 15c. (Etymologically, the word carries a sense of "put (something) under someone else's control.") Earliest appearance of the word in English is as an adverb (mid-13c.) with the sense "under (one's) control," hence also "unrestricted." Related: Abandoned; abandoning.
abandon (n.) Look up abandon at Dictionary.com
"a letting loose, freedom from self-restraint, surrender to natural impulses," by 1822 as a French word in English (it remained in italics or quotation marks through much of the 19c.; the naturalized abandonment in this sense was attempted from 1834), from a sense in French abandon "abandonment; permission" (12c.), from abandonner (see abandon (v.)).

The noun was borrowed earlier (c. 1400) from Old French in a sense "(someone's) control;" and compare Middle English adverbial phrase at abandon, i.e. "recklessly," attested from late 14c. In Old French, the past participle adjective abandoné came to mean "zealous, eager, unreserved."