You'll need a lot of cash and credit cards if you love to shop.  Cannes is well known for catering to the rich and famous so expect to find the best at price in the shops and boutiques.

La Croisette is probably the most famous street for shopping. You'll find shops and boutiques selling all kinds of gifts, fashion and jewelry. Famous designers like Dior and Hermes have shops here. It's also a great spot to people watch as the ocean and promenade are on one side, the boutiques on the other.   Rue d'Antibes is another boutique-lined street in the same neighborhood offering trendy and expensive items.
The Rue Meynadier is another great shopping destination if you're not rich and famous.   You'll find discount clothing and craft shops on this pedestrian walkway.   It's more fun and more affordable. You can also buy some great gourmet foods in the local emporiums including wine, olives and pastries.  

Outdoor flea markets are also popular in Cannes.  Try Marché Forville, the produce market for locally grown fruits, vegetables and flowers.. Marche Forville has an antique market on a Monday, featuring antiques and furniture.

There are several art galleries throughout Cannes. You will find paintings in all of them. There is one gallery that specializes in crystal and glass sculptures. Galerie Daniel Guidat is just off rue d'Antibes on rue Pasteur.  It is next to an artist collective Atelier 11 that is open to the public.  Both are great to visit if you like French art.