Le Carbet has a string of local restaurants along the dark-sand beach, mostly open for lunch and serving Creole cuisine: grilled fish, accras (salt cod fritters), boudin antillais (blood sausage), and colombo (a curry made with meat or fish and local spices). Prices are reasonable by Martinique standards and the setting — plastic tables under palm trees, fishing boats pulled up on the sand — is as good as the food.
For something more serious, the road north toward Saint-Pierre has a few established restaurants with proper kitchens and wine lists. But the beach restaurants are the soul of eating in Le Carbet, and a long lunch here with a Ti' Punch and grilled fish is one of the better ways to spend a Martinique afternoon.