cant give specific recommendations for route, but can say that I do have a fondness for Normandy and Bretagne, but really, if you choose smaller roads and maybe hit the eurovelo route also, you'll have a great time.
Campgrounds are reasonably abundant, and much nicer than when I first did what you are doing back in the early 90s. Crossed France last summer along eurovelo 6 and the majority of campgrounds were really nice, wifi etc.

Im a bit surprised that you dont have an established route only a few weeks off, but hey, like I said, stick to smaller roads and there are so many nice places to see and towns and villages close to each other, that you will have fun no matter.

I used local trains a few times last year to jump distances, and perhaps its cuz i speak french, but it went perfectly well getting the info from train station ticket sellers. But yes, tgv generally dont allow bikes.

have fun no matter where you go, and enjoy the land, the overall respectful drivers, the food and the quiet roads.
As mentioned, you will be there during big vacation time, so campgrounds will be busy, hopefully not full. The french generally bugger off on vacation all at once in aug.