The Académie Française says "jeu video de competition" should replace "e-sports", and "streamer" should become "joueur-animateur en direct".
France's culture ministry told the AFP news agency that Anglicisms were "a barrier to understanding".
But gamers have criticised the ban, with one calling it "completely pointless".
France regularly issues warnings of the "debasement" of its language through imported English words.
Other official translations include "jeu video en nuage" for "cloud gaming".
The Académie Française was created in 1635 by Cardinal Richelieu, and is the official custodian of the French language.
The forty Académie members even have their own heavily embroidered uniform, complete with ceremonial sword - an outfit that might not look completely out of place in a game such 2014's Assassin's Creed Unity.
The institution has long campaigned against the incursion of English words into French, something technology has often encouraged.
However, as news site Thelocal.fr noted, a previous effort to replace "le wifi" with "l'access sans fil à internet", did not take off.
On Twitter, one gamer opposed the latest ruling, writing: "I'm French and I find this absolutely ridiculous, nobody will ever use those terms. This type of ban is completely pointless."
But several others in the same series of replies to a tweet by Eurogamer, posted memes suggesting they thought the French versions sounded rather more sophisticated then their English equivalents.