Try to fly to your destinations. The train rides are tiring and gets old very quickly (esp. if you are in a humid, crowded car sitting shoulder to shoulder). The food on trains is nothing special, just expensive.
Paris is worth at least a week.
If you want to see a "typical" French city, see Lille in the Nord Pas de Calais region. The ppl are less harried there and generally polite. You can cross a street w/o being run over. They have a nice fine arts museum and even a building that has cannon balls imbedded in the facade (from the Napoleonic wars). You'll have to thank the Austrians for that. You can also enjoy everyday French culture, too.
Reims is known for the cathedral and the champagne cellars. I won't tell you not to go there, but there isn't much.
You can also see Nice. It's such a pleasure to walk down those streets. The ppl are also mostly friendly and I still recall those orange trees that line the streets and the view of the Med (first time I saw ocean that was blue and not green). Nice is worth several days of visiting and you could actually spend a week there and not be bored. Be sure to shop at Auchan. A hypermarket like WalMart Supercenters (only larger). You will marvel at how cheap everything is (home furnishings, clothes, chocolates, cookies, foie gras). No tourist book will tell you this, but every French person knows about Auchan.
If you visit Lille, you can take a side trip to Brugge, Belgium. Beautiful old city known for canals. Great chocolates. Don't worry if you don't speak Flemish. Most of the ppl know some English. They prefer to speak this as a second language with tourists.