c. 1400, "a blow" (obsolete), from Old French coup, colp "a blow, strike" (12c.), from Medieval Latin colpus, from Vulgar Latin *colapus, from Latin colaphus "a cuff, box on the ear," from Greek kolaphos "a blow, buffet, punch, slap," "a lowly word without clear etymology" [Beekes].
Meaning "a sudden decisive act" is 1852, short for coup d'etat. In Modern French the word is a workhorse, describing everything from a pat on the back to a whipping, and is used as well of thunder, gusts of wind, gunshots, and chess moves.