I recently completed the trip outlined toward the beginning of the Rick Steves France guidebook, listed as the trip with a car. We followed the book fairly closely, with the exception that we added three days-one in Paris, one in Ile de France, and one in Provence.
I have been to Europe before several times, but this was my first trip that focused on France and attempted to see the majority of it. I think this review may be of benefit to those who may be planning a first time trip to France.
My Overall Impression of the Trip - I do not recommend visiting France this way. There is too much driving time and not enough time to relax and see the sights. The trip also leaves very little flexibility for unexpected things like road closures, weather, and personal issues. You might also find yourself wanting to spend more time at a sight than you had expected or perhaps coming across something you had not planned at all. Unscheduled time will come in handy in these situations.
Here is a plan I think most first-time visitors would like:
Paris - 4-6 nights
This is obvious-most travelers will want to see this fantastic city. Leave plenty of time to go from place to place, as well as time to relax. I am not sure I agree with the Rick Steves suggestion to save Paris for last. You can do Paris first, last, or even split it up to do some nights at the beginning and end. This does require an extra transfer in and out of the city, but might be fun to see how it feels being back after seeing some of the rest of France.
Normandy - 3-4 nights
Most visitors, especially American and British, should include Normandy in their itinerary. The D-Day beaches are deeply moving as is MSM. A "quick trip" to the beaches is not a realistic idea as sites are not all close together. I would also suggest a visit to Rouen or Honfleur if time permits. You can go by rail or car or both.
French Countryside -
I would suggest picking 2 or 3 other spots (or more depending on how much time you have) and taking the TGV from Paris to the countryside locations and back (a wheel and spoke type plan). While this does require backtracking a bit, the time on the train provides time to relax or catch up on guidebook reading or whatever else.
I would only consider the plan of driving in a loop around France if you have at least four weeks, and even then would cut out one or two of the stops listed in the Rick Steves list.
If your primary interest is Southern France, consider just going there and saving the North for another time.
Nights needed in each region:
Champagne 1, (Reims can be done as a day trip from Paris)
Alps 2 at least
Carcassone 1 will do
Loire Valley 2
So, for an example, after you finish Paris and Normandy (about eight nights, don't forget the night to fly in most US travelers will need):
1. TGV to Avignon for 4-5 nights in Provence
2. Back to Paris and then TGV to Burgundy for 1-2 nights
This can be done until the length of the vacation is ideal for you. My favorites were Dordogne, Provence, and Alsace.
I strongly recommend including the countryside in your vacation, rather than spending all the time in and around Paris. It will add considerable depth to your experience. Do not try to do too much. You need time to take it all in. Have a day or two with basically no plans.
Have a good trip.