Trip to France with 2 preteen girls

If you do not have a guide book, such as this--- https://store.ricksteves.com/shop/p/best-france-guidebook--- you may want to get one, RS or otherwise, and look at what interests you. You look to be stretched a bit thin in what you outline above, insofar as the number and location of your desired destinations.

Will you fly into Paris and out from Nice/Marseilles? Or do round trip flights into/out of Paris. If the latter its pretty much a full day of travel (car or train) from Nice to Paris and you should spend the night in Paris before your return flight rather than try a long distance commute on the day you fly.

Since you will not have any help with driving it likely would be more relaxing if you used trains, which look to go to all your destinations.

I guess I was looking for ideas about where to go after Paris.....
Since it is the three of us I thought it might be cheaper to rent a car and drive to the next place to stay and use as a base for day trips, then yes head back to Paris and stay near the airport the day before we leave.

You might think about taking the train, if you have a great distance to cover.
Marseille will take you about 3h17 mins by TGV, much longer if you rent a car.

You have lots of time to plan for tickets. Look for prices 90 days in advance on this website:
http://www.sncf.com
You will have to reserve seats for the TGV.

Another handy website is this one, which explains all about European train travel:
www.seat61.com/France-trains.htm

Assuming you are flying trans-Atlantic, do not go back to Paris to fly home. Instead, use a multi-destination search function on agency or airline sites to fly into Paris and home from Marseille. You will save the time and expense of going back to Paris. The flight itinerary out of Marseille will probably include a change of planes. For that reason, I would reverse your timetable and fly into Marseille to begin, work your way back to Paris and fly home from there. You won't have to get up as early in the morning to catch the trans-ocean flight home.
Buy all tickets now. Long-distance trains and airplanes are cheapest when bought well in advance. I use https://en.voyages-sncf.com/en/ Note that seat reservations will be included in the tickets. Seat 61 is the authority for all rail travel. Some Americans have credit-card obstacles with SNCF; an alternative is www.trainline.eu
I'd prefer Marseille to Nice, for easy day trips to Avignon, Orange, Arles. In France, every city, town and region has eager government-run websites to help you plan your time. The kids can help with the research.

Three things to consider. First, get the girls actively involved in the planning. The more they are involved the less likely you'll wind up with "unhappy campers" on your hands. Second, personally I'd forget about renting a car and do it all by train. Others will disagree, but to me renting a vehicle and then doing the driving is just too much hassle. Third, with your time frame pick out only two places other than Paris. It's amazing the amount of time you'll lose just getting from one place to another.

If your target is Provence, I would not base in Marseille. I think Avignon or Arles would be more convenient--less time on trains making multiple trips north.

Sounds like a fun trip. We went a few years ago with our two pre-teen granddaughters. I agree it's good to involve them in the planning just to stimulate pre-trip excitement. Our granddaughters each picked a "must-see" place in Paris and one or two works of art they wanted to see. Of course, you're the adult and will understand both attractions and drawbacks in ways that they won't.
Our girls loved the catacombs. Just make sure you get there early. Even up to 45 minutes or an hour early. That may seem like a long time to wait before the doors open but it's nothing compared to how long you'll wait if you get there even 20 minutes after opening. They also loved the Eiffel tower and were thrilled to go all the way to the top. We ate in the Eiffel tower but I wouldn't consider it necessary. The food is expensive and unremarkable (and you did mention staying on some sort of budget).
We like Chantilly but consider Vaux-le-Vicomte as an alternative.
Consider a Museum Pass for yourself (most Museums are free for kids). They're costly but we love them if for no other reason than for popping into Museum bathrooms.
By all means get a car. It will, as you say, be used for local trips as well as "getting there." And getting there doesn't have to be considered time you'll "lose" just getting from one place to another. Why should travel time be "lost"? Look up what's along the way and stop to enjoy. As experienced travelers, we enjoy taking the train but I wouldn't suggest it in your situation. You have to factor in getting to the station (with all your luggage), and getting around once you get off the train (with all your luggage). There are some "tricks" to driving in France, which I'll be glad to share in more detail if you wish. The short version is (1) don't speed and (2) remember that road signs direct you to the next village or the next large city along your route - they do not show you route numbers. And, if you should get lost, don't panic, just get "found." Stop, re-orient yourself and get back on the proper route. No biggie. It's France, not Afghanistan.
Hope this helps. Please free to private message me if you want more details. I'm sure your and the girls will treasure this trip.

Are there things you want to see and do that require a car? If so, a good strategy might be to use a train to get to the region in question (Burgundy, Provence), and a car to explore.

That time of year can be cold and wet. Any hopes you have for seeing hills or farms or beaches should be backed up by a more-urban plan B. So, know what you will do on the day it rains in Provence (if you go there).

May I suggest Lyon? It is on your route and is just a really great, fun place. I like it better than Dijon, not that you have to choose.

There is something for everyone there: Roman ruins, great food and shopping, a funicular, a boat ride, an an old town riddled with secret passages. You could easily spend 3 whole days there. Check it out in a guidebook that you trust.

I'd definitely read about the mistral before deciding on Provence.

Lyon or Dijon would be my choice. There's lots to do there...and you won't need a car.