Wow, don’t know which tips to give because France is big and there is a lot to do and see. That it will be fun is a certainty. Don't think about the time you have: you can never see everything and you can always go back. Some good tips have already been posted and Bison Futé is a nice one: when I was a child my parents drove to the South with the camper via this route and I always followed along on the free map that you received at the stops along that alternative route. Pure nostalgia. The route was there to relieve the busier roads, but they were sometimes very busy themselves. The péages are easy and a cali can go under 2m barriers so not too expensive. The stops are sometimes an experience with animation and many people (so pay attention).
So the south is your target? It can and will be warm, but this does not have to be a problem because the Ricard will taste even more. We often alternate the pieces of péage with beautiful route nationals (RN or N). We use péages to get from a to b faster and especially during the pieces where I know you don't get ahead smoothly on other routes. Mind the speed cameras at the many villages you will cross.
Whether you will be on campsites or camperplaces: all can be found with apps such as Park4Night (it doesn't sound like that, but it's French).
I don't see a problem with priority from the right because with us it’s a basic traffic rule: you let those coming from the right through unless traffic lights or other traffic signs show that you are driving on a priority road. Pretty simple. Apparently some are not used to this because you drive on the left and you should not give way to those coming from the left.
Anyway, I'll try to give some tips, you can look it all up and make your own idea about it.
Less than an hour's drive from Caen: Deauville: walk along the dike and feast your eyes on old but not yet completely faded glory. Le Mans: already mentioned by someone in another post but indeed, if you're a car or racing fanatic, be sure to drop by: the museum is brilliant and you can walk along much of the track and see famous places; recommended. My next tip is a difficult place: Oradour-Sur-glane; you will be impressed.
Then you can drive through some nature reserves such as the Regional Natural Park Millevaches and Limousin, Parc naturel régional des Volcans d'Auvergne including the Puy-de-Dome Volcano (train, walking) and then further south through more nature parks.
You can visit some French coastal cities in the south and the French Riviera/ Côte d'Azur is nice to drive and also visit some places, good food and not expensive, don't forget Monaco: special to see (Drive your cali to the center and park it underground: dirt cheap).
Also south, but not the coast: Ardèche, Millau viaduct, Gorges du Tarn, Montségur, viaduc de Gabarit, Pont du Gard, or: Frensh whisky:
https://distillerie-castan.com/en/ and many more.
I don't know exactly where you want to be in the South of France, but I can recommend the Camargue and certainly the region just before it: 'le petit Camargue' with Aigues-Mortes and many others. Some places will not be busy at all and some roads even seem desolate, other times you will be among the locals or plenty of tourists. All situations with their own charms.
A lot, I know but if it is not for now, then for another time.
Enjoy road tripping in France.
www.bison-fute.gouv.fr
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