We will spend 3 nights in Paris with our kids, 13 and 15. Then one night in the Burgundy area and 2 nights in Provence. Please let me know what not to miss!

3 nights in Paris (including the arrival day, I presume), 1 in Burgundy, and 2 in Provence? You'll be very hard-pressed even to catch a few of the absolutely main sites in each area. And without knowing what your interests are, it would be very hard to pinpoint those few things you shouldn't miss.

Where in Provence are you headed? Why are you headed there? What do your kids want out of this trip? Have you/they done any research thusfar?

We'll have 2 and half days IN Paris, and then an extra day to see Giverny and Versailles. Burgundy we want to see a winery or 2, relax, and basically break up the driving trip to Provence. We plan to stay near St. Paul De Vence for 2 nights/3 days at Le Hameau. (then we drive to Italy...)
Yes, I have guidebooks and am researching. I'd love all the advice I can get!

I think this would be a doable day-trip if you want to go a bit farther from St. Paul de Vence and if you really have 3 full days of time in Provence... I suggest Les Baux de Provence. I took my kids there and they loved it. You walk up to the top of the town and there is a great fort/castle with gigantic midieval weapons such as the enormous catapult. (Great view too) Nearby is the Cathedral d'Images. That was closed when we were there, but if I recall correctly, there are hundreds of images cast onto cave walls along with music. Maybe someone else can comment if that is worthwhile, but it sounded good to us. Maybe the kids won't like this next suggestion quite as well, but since it is nearby, my mom and I enjoyed the Musee des Santons, a museum of large animated santons (the figurines mainly displayed at Christmas) and of course small shop. It wasn't much out of the way and didn't take long. We passed a few tiny roadside shops selling the tiny handmade handpainted clay santons, which I bring out every Christmas. It was fun stopping in the middle of the country to buy them. My husband visited a winery when I was in the museum. Very good wine!

Thanks, Kwren. That sounds like a great side trip. I'll look into it. Do you know how far Le Baux de Provence is from St Paul de Vence? We will have a car.

Rent Segways in Paris or take a bike ride w/ Fat Tire Bike Tour. FUN!! http://www.fattirebiketoursparis.com/(Several threads already on Fodor's)

Be sure to go on a boat tour of the Seine while in Paris.

Let them pick a new "Parisian" outfit at a funky store.

Eiffel Tower, bien sur.

Creperies in the Latin Quarter for a late night sugar fix.

The fountain at Centre Pompidou for the people watching experience.