Planning a trip to France for all of July. We will fly to Paris, spend a week with day trips to Vers

Planning a trip to France for all of July. We will fly to Paris, spend a week with day trips to Versailles and potentially Normandy. Perhaps we should stay a night in Bayeaux or there abouts? Hoping we can do all this with trains. Then would like to go to Dordogne. Wondering if it is best to rent a car or can you do this region with trains/buses? Or perhaps a combination of the two. May take a TGV to Lyon and then car or train over to Sarlat. My thought is the trains are faster, but the car would allow a lot more freedom to explore, but would be slower. I dont want to spend all our time stuck in a car. Do the trains allow you to enjoy the scenery, or are they too fast for that? Also, I'm worried about getting stuck in the middle of nowhere if trying to do train/bus. Would like to then spend some time in Provence. I've been looking at JoJo's trip report from 2009 and getting ideas and inspiration from that. I know this isn't super specific at this point, but would love some comments on the pros and cons of different travel modes. Thanks
You need to get a better idea of what you want to do. In general, if you want to see the big cities, trains are better, because cars are a liability in cities. On the other hand, if you want to explore small villages, then you need a car. Or, you can do a combination. Take the train between the cities, then rent a car for staying in smaller places and taking day trips from the cities. But you should try to get your lodging figured westin hotels home page out soon, as July is a busy month, especially in Normandy.
Normandy is much more than a day trip from Paris if you're interested in the D Day beaches, the museum in Caen, and the tapestry. You can take a train and stay overnight in Bayeux but would need to book a tour to visit the beaches.