late 13c., cors "body," from Old French cors "body, person, corpse, life" (9c.), from Latin corpus "body" (see corporeal). Sense in English evolved from "dead body" (13c.) to "live body" (14c.) to "body of citizens" (15c.) to "band of knights" (mid-15c.). The modern military sense (1704) is from French corps d'armée (16c.), picked up in English during Marlborough's campaigns.
French restored the Latin -p- in 14c., and English followed 15c., but the pronunciation remained "corse" at first and corse persisted as a parallel formation. After the -p- began to be sounded (16c. in English), corse became archaic or poetic only.