Planning 15 day family trip in June - Paris, South of France?

If you spent your first five to six nights in Paris, you can take the TGV to Aix-en-Provence and then head to the countryside (Luberon) for a few nights. You can then drive to Nice to complete your stay. Return your car and use public transport, unless you are staying out of coastal area. Nice is the most centrally located, with the best transport links. Antibes/Juan les Pins is another choice, if the beach is a top priority (otherwise do it as an easy day trip).

I assume that when you say 15 days you are including travel days, so 13 for touring. If you do 5 in Paris, you could take the TGV to Avignon or Aix, get a car, and spend 4 or 5 days in Provence. After that, spend the last 3 or 4 in or near Nice.
Check into return flights from Nice. I’m sure we’ve done that at least once. It will save you a day that would otherwise be spent getting back to Paris. Even if it’s somewhat more expensive, train tickets aren’t free, and you would probably have to pay for an overnight stay, as well.

Paris plan sounds good

Really your decision if you want to include Provence sites or stick with the Cote D'Azur area. Either way I think you have enough time to make a plan that works.

If you decide yes to Provence. Take the TGV train from Paris to Avignon.

I believe after Avignon the train is not high speed so it is much faster than a car to Avignon but no faster after that.
You have to make the call with your wife's motion sickness, absent that fact I would say rent a car in Avignon and drive it to Nice. Lavender fields may be in bloom which you would need a car for as an example plus the little hill towns there are best seen that way. Hand it off in Nice and use public transit for the last 5 nights or so in Nice or nearby town.

if you decide to skip Provence and spend more time on the Cote D'Azur than I would fly. I went back and forth on train to Nice or flying from Paris and with the cheap Air France flights from ORY airport I think the flight is a better choice or at least saves a little time and does not cost more in our case. You can make a case for either transport method but definitely do not drive from Paris to Nice that would be a waste of time and not save anything unless you plan multiple stops in route that you really wanted to see.

As far as a base for the Riveria, Nice is the best in terms of being a transportation hub so make sense for most but there are many connected via rail towns nearby you could stay at instead depending on your interest.
Villafranche, Anitbes, Juan Les Pins are 3 popular alternative towns close by.
For me, I mapped out what I wanted to do in the area to see if I was better of staying slightly to the West of Nice or slightly to the East of Nice. Monaco for example is to the East of Nice.

Main decision for you is Provence or not, if yes fit it in the middle since doing it any other way would not be logistically as good.

No car necessary, all easy by train ...

Day
1. Arrive Paris (6)
2. Paris - non museum pass sights
3. Paris - Museum Pass Day #1
4. Paris - Museum Pass Day #2
5. Paris - Museum Pass Day #3
6. Versailles - Museum Pass Day #4
7. TGV train to Avignon (3)
8. Day to Nimes
9. Day to Arles
10. TGV train to Antibes (5)
11. Day to Cannes & Grasse
12. Day to Monaco
13. Day to Eze & Villefranche sur Mer
14. Day to Nice
15. Depart Nice

If Provence is a shortish stop then Avignon is easiest as it has the best train connections.
Antibes has the best beaches along the Riviera and also offers good train connections.

I agree with the other comments but wouldn't consider interrupting my vacation serenity (such as it is) by dragging myself to Orly for a flight. However, timewise it could go either way. When comparing costs, don't forget to look at the fees for checking bags (if yours don't meet the lower European carry-on limits) and seat-selection if it's important that you all sit together.

I used Aix en Provence and Avignon as my bases in Provence without a car, but it would be great to have a car there. If you decide to go that way, I encourage you to make use of the vehicle by going to places that are difficult (some virtually impossible) to reach if you're stuck with just trains and buses--places like Gordes, Roussillon, Les Baux and the like. Those are touristy in the sense that bus tours go there (so they probably are the most dramatic); others here can probably suggest options that are also worthwhile but less visited, if you would like a somewhat more peaceful route. It's not that I didn't like the larger places, but they can be done without a car, as can L'Isle-sur-la-Sorgue and St-Remy.

Note: Hill towns do often require transiting curvy roads, and I have occasionally suffered queasiness on those when I was sitting on a bus. I can't speak to Provence, really, since I didn't tackle much in the way of challenging terrain.

It would also be reasonable to spend all your non-Paris time along the Riviera. It's something I would consider very seriously if, as you plan, you find your day-count in Paris creeping up. Provence and the Riviera are quite different experiences and both totally worthwhile, but at some point, the time spent relocating needs to be considered.

You can move along the Rivera coast quite well by train, though if you want to visit locations down on the peninsulas (Cap d'Antibes, Cap Ferrat, etc.), you'll need your feet, a bus or a taxi. The hill towns (Eze, Vence, St-Paul-de-Vence, Biot, etc.) genearlly mean buses, though I think there's a train up to Grasse. I am afraid those buses would be problematic for your wife, so you may prefer to stick to the coastal towns. In addition to those already mentioned, I liked Menton a lot. It's all the way east near the Italian border. It does get a lot of tourists, but the historic district is impressive and there are two very nice gardens. Both of the latter are on hillsides, so good footwear is recommended. You could even take a train all the way to Sanremo in Italy.

I liked staying in Nice for the many museums, the old town and the markets along the Cours Saleya, but it is a without doubt a city. Staying in a small town would make for a different experience. You can check travel times on the Deutsche Bahn website to be sure the place you choose as a base is reasonably convenient to the other towns you want to see. For fares you need to consult SNCF. You'll save a lot of money on long-haul tickets (e.g., from Paris south) by buying early. For short hops along the Riviera, it doesn't matter. Note, though, that lines at both staffed counters and ticket machines can be long at the Nice Ville train station. I missed a few trains while waiting to buy tickets at those machines, and I was there in May.

June is not yet quite peak season along the Riviera, so you should be able to find a nice place to stay that won't break the bank.

Remain alert for pickpockets on the trains along the Riviera. They are active there.

Airfares are higher this year than last, but Nice is sometimes an affordable city to fly into or out of, so it's worth checking multi-city fares into Paris & out of Nice. Edited to add: Or vice versa. By June it's rather warm in southern France.

Rick has a book on southern France that would be very helpful in planning your assault on the area. The coverage in the general "France" book is good, but less complete.

I'd plan to take the train to Avignon or similar and spend a good 4 or 5 nights in the Rhone Valley. Get a car and visit some of the places that are not well served by rail. Pont du Gard, the Camargue, Fontain de Vaucluse, Les Baux.

Don't stay in Avignon, but not in Aix either, it's too far from stuff. Some popular bases: Arles, St. Remy, Isle sur la Sorge.

The balance of your time in Nice. Decide if you need a car there; you probably don't. Flying home from there is very smart. Have a blast!

Thank you all for the very useful and detailed suggestions. This is a great resource. I’ll discuss with my wife and daughter.

I understand there is a registration number I should have for Airbnb rentals. Anyone know where to find it?
Thanks again.