There are plenty of restaurants, cafes, bars, gelaterias and creperies in the South of France to take little ones.
Cafés, bars and restaurants are available to meet almost all price-points and most tastes, however the vast majority of eateries serve food local to the area – that is to say Provençal cuisine with influences from Italy. Pizza restaurants generally serve pizza with a very thin base. Asian cuisine – Indian, Thai, Chinese, Japanese etc. is available but is not common outside the main seaside towns.
Bouillabaisse and Salade Niçoise are perhaps the best known local specialities although there are others such as Socca. The surrounding mountainous area makes a number of (mostly goat or sheep) cheeses which are usually available in local supermarkets as well as at market stalls. The Riviera has a number of olive oil mills and a lot of olive trees.
People tend to eat late in France however, you will be able to find restaurants open earlier in the evening. Some of the more up market restaurants may not be welcoming of younger children, particularly in the evenings so do check in advance if you are unsure.