Nancy and Vandoeuvre have several options for grocery shopping Ex. Lidl, Match, Chinese Supermarket, Local Markets. Following some direct links with the locations:
In addition the city has a wide variety of malls and shopping stores in order to find them you only have to walk from the Tram stop: Nancy Gare towards the station Cathédrale.
If you need a bigger market, two solutions are available for you. The simplest one is Auchan Lobeau, situated not far away from the center and the Provençal accommodation.
The second solution is Cora Houdemont. It is situated outside the city, but you can take the bus 17 to get there.