You can say "faire du shopping" if you buy clothes, make up, shoes etc ... And "faire les courses" if you buy food or domestic products. French people usually use "shopping" to talk about a leisure, and "courses" to talk about an obligation (obligation of buying food, etc ...)
rest from shopping in French is: reste des boutiques
Shopping center in French is : un centre commercial (masc.)
achats
we say: centre commercial
achats attend
Revoir achats
j'aime faire les magasins / j'aime faire du shopping
les courses de Noël
'mall' means what it means: a 'shopping mall' if you're asking how to say 'mall' in French: then it is 'Mail' or 'centre d'achat' for shopping centre
"un petit centre commercial"
It should be something along the lines of magasin de vetements which is clothes shopping.
est-ce que vous faites les magasins