English picked up "volant" from Middle French. The term survives in Modern French as well, both as an adjective having essentially the same meaning as the English term, and as a noun with several meanings (among them "shuttlecock"). The influence of French can be seen doubly in the heraldic sense of "volant": in heraldic contexts the adjective "volant" almost always appears after the noun - a syntax picked up from French along with the meaning. Ultimately, "volant" comes from the Latin verb volare, meaning "to fly." Another word that came to English through Middle French from volare is "volley," which refers to things flying back and forth through the air.
