The Jura will be quiet apart from the lakes. The Summer is surprisingly wet.
The Loire valley has enough campsites to mop up the tourists without ever feeling too busy. It's a long river, the bottom is flat and boring, then comes an interesting bit with castles and towns to visit, the top is wild and pretty much deserted.
Brittany is tourist land around most of the coast with real tourist traps along the south coast. Booking is a good idea. The weather is similar to the UK but a little warmer.
What do you intend to do with your days? Walk on a beach and chip at blocks of hercynian granite, paddle muddy rivers or visit deserted ski resorts.