Some of the big hypermarkets (Carrefour, Auchan, etc.) have an "exotic foods" aisle, but their selection can be fairly limited unless you're in an area where there are lots of recent immigrants. (Our local stores seem to concentrate on Portuguese and Moroccan delicacies. Their selection of "Chinese" is limited to fairly standard items.)

There's always the possibility of making a run (monthly, quarterly, ??) to Paris, where you can shop in the Asian district (near the porte d'Italie). Teng Frères is well known and well stocked with foods and nick-nacks from most Asian countries including many produce items you can't get in most French supermarkets. (Their prices are also very good.) There are a number of smaller stores in the same neighborhood - though lately it seems like they all belong to Teng Frères.
Cheers,
Bev