All of them are great - but it depends what you're looking for and what you want for your children. Brittany is like Cornwall, so if you want great beaches, and pretty villages this is the area to go for. The Loire, Burgundy and the Limousin are gently rolling hills, interesting towns, and Chateaux, with the great rivers of the Loire and Dordogne. The river Dordogne is great for canoeing and there are some lovely campsites there, with lots of British visitors. It's generally said that the further south you go the better your chances of great weather - and the Dordogne is the furthest south. However, last year almost everywhere in France had poor weather during the school holidays, so it's by no means guaranteed.
If you've never been to France before, then you'll find all areas have great campsites, with good facilities. You can find anything from 'Camping a la Ferme' to 'All-singing, all-dancing 4 star sites'. In peak season (mid-July to mid-August) the bigger sites get booked up pretty quickly, so you may need to look at booking if you're going during this time. If you're going later in August then you should find plenty of pitches still available. If you want lots of other British children around then look at sites which have 'tour operators' such as Eurocamp, Keycamp, or Canvas Holidays.
If budget is a real priority then you could look at the Camping Cheques website www.campingcheque.co.uk - which offers sites for