feud (n.) Look up feud at Dictionary.com
c.1300, fede "enmity, hatred, hostility," northern English and Scottish, ultimately (via an unrecorded Old English word or Old French fede, faide "war, raid, hostility, hatred, enmity, feud, (legal) vengeance," which is from Germanic) from Proto-Germanic *faihitho (compare Old High German fehida "contention, quarrel, feud"), noun of state from adjective *faiho- (cognates: Old English fæhð "enmity," fah "hostile;" German Fehde "feud;" Old Frisian feithe "enmity").

This is from PIE root *peig- (2), also *peik- "evil-minded, hostile" (see foe). Sense of "vendetta" is early 15c. Alteration of spelling in 16c. is unexplained. Meaning "state of hostility between families or clans" is from 1580s.
feud (v.) Look up feud at Dictionary.com
1670s, from feud (n.). Related: Feuded; feuding.