I agree with others, stick to Paris with day trips (like Versailles). You really don't have time for all the moving around you'll have to do to add Provence (where?) and Nice.
The "Explore Europe" link in the upper left of this page will take you to France, and to Paris, with good suggestions for sightseeing priorities and itineraries, especially in Paris. But consider your own and your daughter's interests rather than just following someone else's path. Build in some down time each day for parks, cafes, strolling, people-watching. Take a Seine cruise (I like Vedettes du Pont-Neuf). Take some city bus rides just to see the streets, #69 is a good route that links a lot of sights and scenes.
It will be hot in August so a hotel with air conditioning will be a big help. Hopefully you'll have some choices if it's this August, certainly you will for next year.