In addition to Bar des Oiseux, look for Bistrot d'Antoine or Comptoir du Marche. Reservations are a must. These are in the touristy old town but are popular with the locals.
Just around the bend, in the Port area, try Jan for high end or Les Pecheurs or L'Ane Rouge for mid range. Les Amoureux for Pizza. For a good view of the water, La Reserve is a classic but pricey. For an acceptable meal at a much lower price with a great open water view, Le Plongeur.
Of the beach restaurants (on platforms on the beach), the Beau Rivage is among the better ones although I heard the new Le Galion is pretty strong. In the Carre d'Or, Cafe Sejour is highly recommended. Coco et Rico is good, and many people do like Le Franchin.
The local food market referenced above is Liberation, and is readily reached by the Tram. The antique market is only on Mondays, when the regular food market takes the day off. On wednesdays there is the equivalent of a flea market in Place Garibaldi.