I have yet to visit Reims and the Champagne houses; tgv gets you there in about an hour. Also in my bucket list is Lyon, easy train. I took the RS tour of Paris and the heart of France last fall; look at the trip to see what you might do on your own. I loved Amboise and the chateaus. Bourges was great and I would return for longer; we only had a one nighters there. The cathedral there is fabulous. Mont st Michel is very romantic, stay the night to get the full experience.
You could stay in Paris the whole time. I am returning to Paris for 3 weeks this fall and love it. So many day trips to do. Search this site for day trips from Paris. There is a book of that title too, or something very similar.
Last fall I joined a photography meetup group and did a couple of things with them. We visited a night market that I would never have known about in my own, food, music. Paris Photography is the name, there are probably many of them. If you pm me I can give you names of the organizers so you know which group I am referring to. Many are expats so English was spoken. I also visited a beautiful park that I did not know about and walked around with a very interesting retiree. The. The group meets at a cafe for a drink of whatever you like. Very civilized! This was the first time I had used Meet Up. I still get the group emails and will join them this fall too.
I love Villefranche sur mer, 5 km from Nice; that is an almost 6 hr train trip from Paris. Cheap airlines might get you to Nice faster. So many things to see by bus or train from Nice or Villefranche. Search this site for Villefranche, a RS tour introduced me to the town over 10 years ago and I am visiting for the 4th time this fall. A nice sand beach.
Enjoy your trip