Where to go after Paris

My first thought was Alsace, but it's way beyond your driving-time limit. I'm not clear about the car situation. Will you be keeping the car while you're in Paris? If not, trains will get you to Strasbourg in about 2 hours, and you could rent a car if you want to visit vineyards and small towns.

We will not rent a car until we are ready to leave Paris and will return it to the airport.

In that case, consider taking a train to the region you want to visit, picking up and returning the car there. That will open up a wider range of potential destination. The train can be affordable if you are in a position to buy the (non-refundable, non-changeable, train-specific) tickets early. I don't know when you're traveling.

I would recommend Lyon. It checks the box on food and wine. While not in itself a great wine producing area, it's close to the Beaujolais and Rhône wine regions (with Bourgogne, Savoie, and Auvergne not far beyond those). Compared to many places in France, Lyon is more businesslike and is not as overrun by tourists (except for Vieux Lyon). A lot of kids studying in Annecy spend a day or two in Lyon, but with some planning you should be able to fill your schedule with interesting, memorable activities your daughter likely had not seen. Lyon has its own attractions, but also nearby is the medieval town of Pérouges and the partially-excavated Roman town of Viennes. For physical activity, there are walks, runs along the Rhône and Saône rivers, and both walking and biking in the beautiful and quite large Parc de la Tête d'Or (Lyon had one of the earlier bike rental networks in Europe and it's very convenient, even if the bikes are a bit, err... sturdy).

If your daughter had spent time in Chamonix, check to see if she had seen Mur du Glace or taken the télépheriques to Aiguille du Midi and on to Hebronner. If not, it is absolutely worth an overnight visit. You can drive to Chamonix in the afternoon, spend a night at a hotel, and get up early the next morning to see Alpine peaks, glaciers, and glacial landforms that are truly astounding. You can do all that by mid-afternoon, and head back to Lyon with memories that will last a lifetime.

After CDG and Orly, Lyon's Saint-Exupery airport is a pretty good point of departure for elsewhere in Europe.

I lived in Lyon for a few years until moving to Bourgogne, so if you have any specific questions feel free to drop me a message.

I would rent a place in Burgundy if you can find one in a small town or even an agro that rents for less than a week; this is such a beautiful area. We spent a week in Semur en Auxois and day tripped via car from there; it was enchanting.
https://janettravels.wordpress.com/2010/08/25/medieval-towns/
If I were you I would start in Burgundy (or wherever you decide to go) and finish in Paris to fly out. e.g. take a train to Dijon and spend the night the afternoon of arrival and pick up a car the next day for Burgundy. Or take a train to Tours in the Loire and do the same. You could drop the car coming back into Paris and finish in Paris. By doing it the way you plan you waste your second to last day of a very short trip rushing back to Paris for your flight. If you are stuck with Paris arrangements then I would come back the afternoon of the second to last day, drop the car, check into the Novotel or other airport hotel and then take the train or a cab into Paris for dinner and a nice stroll along the river and then be at the airport for the flight. Never try to drop a car at an airport just before a flight unless you are prepared to buy walk up tickets -- traffic, difficulties with rental return etc are all more likely than you would think.

Well, I think your whole trip will be better if you drop the idea of driving everywhere.

Taking the train puts Provence well in reach, for example. You'd want wheels once you get there, but the train is a lot faster than a car on that route. There's an international airport in Marseilles.

Provence will include crowds and uncrowded places. There are plenty of nice walks and hikes to take in the Luberon.

Burgundy is also a fine idea, especially if you are up for biking.

Lyon is fabulous, but of course is a city. With an international airport. If you ended there, you could just fly on without difficulty.

So I think you have a lot of options!

Thank you all for your suggestions. Can you recommend a "home base" in Provence, Luberon or Burgundy?