We live in the Dordogne, it is incredibly popular during the summer, best time to come is last 2 weeks of august as the French are pretty traditional about taking their holidays in the first 2 weeks of August, and also last 2 weeks of July. Also it is not quite as blisteringly hot.
As mentioned there is lots to see in the Dordogne, but it may be better for slightly older children, say about 8yrs + Most of the campsites have swimming pools, and there is canoing, markets, gorgeous villages, loads of caves and chateaux to visit.
Bordeaux is a beautiful city, like a mini Paris, so again good for older children. You are also very close to the wine region with simply stunning chateaux; Rothschild, Latour etc.
Close to Bordeaux is Arcachon which has fantastic white sandy beaches and the largest sand dune in Europe. Dune de Pyla. It is very popular with french holiday makers(again be aware of the dates.) The sea is really clean, although can be a bit bracing even in august.
I think Ile D'oleron is great for families. There are loads of car free cycle paths, huge sandy beaches, lots of little local markets. There is a big water park on the island, Horseriding, wind surfing, kayaking, widllife sanctuary. La Rochelle is less than an hour away and the aquarium is defintely worth a visit. La Rochelle has lots of lovely shops, reasonably priced restaurants and a big marina and harbour.
(Ile de Ré is nearby, but there is a big toll about 16 euros to drive onto the island.) St martin de Ré, the capital is very pretty, but the rest of the island is no better than Oleron. Ile de Ré is full of Parisians on their summer hols so has that snob factor, but it is worth a day trip visit.