Bougna, a traditional meal among the native Melanesians, which consists of some form of meat, pork, chicken, fruitbat, crab, etc, along with roots such as yams and sweet potatoes. This is wrapped in banana leaves and cooked under hot rocks heated in a fire.
Coconut crabs
fruits
All fruits seem to taste very good
Buy food from local markets, which are common to almost every town.
Restaurants are expensive. You can eat quite well for about 10EUR at a couple of eateries opposite the library in town. For travellers on a budget, you'll need to observe what the Kanaks do for the best deals.
French food is obviously a specialty, but the range of foods available can be a little limited.