If he has a house in France then, presumably, he has a Carte de Sejour.

Armed with this, he should go to the local Gendermerie and apply for a permis for a rimfire (a Modele No 10 - Declaration d'Acquisition/Possession Des Armes)- a mere formality and free of charge.

He may need a doctors cert to say he's medically fit/sane - but that depends largely on the departement he lives in. If the Gendarmes are feeling in a good mood they'll tell him to go get his rifle and drop by with it as soon as it's bought. They'll fill in the form while he waits (20 minutes, tops)

With the permis he can pop down to his local Armurier and buy a rimmie for half the price of an air rifle and send his rabbits to Valhalla.

Regards
BC