I love the Charente region. never quite made it to the coast though - I do want to visit La Rochelle and the Ile de Re.
Dordogne has beautiful scenery. Lots to see also.
Languedoc is a long drive down, but I like d it there too. If you get that far south, Carcassonne is a must. That will impress your American friends !
This year we were in Normandy for a few days - Bayeux and the D Day landing beaches etc Then in the Loire valley in a rented house for a week. Very beautiful also.
Our DC are teens, so a bit different to your group.
I imagine th at wherever you end up, if you have somewhere with a pool, and a few play items for the DC they will be happy.
The year we went to Llanguedoc we stopped off in Paris on our return home to the Tunnel. But we hired an apartment privately for 2 nights, which was much easier than hotel rooms - it's a pain taking 3 DC out for restaurant meals all the time.
If you look on the rental sites - such as Home Away.co.uk - you will find gites for rent - some of which are better than others for young Dc.