Travel between Paris to Nice

Wow .... I think I'd skip Nice since you only have 10 nights. Paris, Normandy and Bordeaux makes sense together and a great trip for 10 nights..... add 3-4 more nights and add Nice and fly. I'd fly into Nice.... then fly Nice to Paris and train the Normandy/Bordeaux part.

Nice and the Riviera is well worth it, but it's a long way for such a short trip, I'd likely stick to the North if it's only 10 days. If you do want to fit it in though, we took the train from Nice to Paris in 2019 and it took about 6 hours. There was no cost savings compared to flying, but probably no time savings either if you consider the time it takes to get to the airport, through security, etc.

Ten nights is too short a time for your itinerary. After Normandy you can explore Brittany and then Bordeaux.
We did Paris, Burgundy, Provence and Cote d’Azur( Nice) but had a full month.

France is a very large country. It's not practical to cover it from stem to stern in 10 nights.

Is this your first trip to France? How much time do you plan to spend in Paris itself? If this is a first trip, I'd guess you'd want at least five nights there; your arrival day is likely to be significantly marred by jetlag and sleep deprivation.

What do you want to see and do in Normandy? Some folks just head that way for the invasion sites (in which case I recommend staying in Bayeux and taking a full-day van tour); others want to see Honfleur (no rail service), Rouen, etc.

Train lines in France tend to fan out from Paris. To travel from Normandy to Bordeaux, I think you'll have to go through Paris and change stations there. That's doable but adds time.

What is your interest in Bordeaux? Some people go for the wine; others head there en route to the Dordogne. The latter's a very interesting area, but some use of buses is required, so it's not an area you can visit quickly.

There isn't fast rail service between Bordeaux and the Dordogne and the Riviera; Bordeaux to Nice is at least 9 hours by train--an entire day of your trip gone.

The Riviera has lovely coastal towns and pretty hill villages. Nice is the transportation hub, but there is a local (not express) rail line running through nearly all the coastal towns. Lots of things to see down there; Nice alone has at least six art museums, just as one example.

The return trip from Nice to Paris takes nearly six hours by train.

I agree with the others that with only 10 nights I'd stick to Paris, Normandy, Bordeaux. If you could add a few days, then you could do Paris, Normandy, Bordeaux, then fly to Nice and fly home from Nice. But I wouldn't do this without a full two weeks due to the travel distances between these places.

Thank you, everyone. We are now thinking fly in and out of Paris. Spend a couple of days there (we are not looking to spend too many days in Paris). Then head to Normandy. Yes to Roen and Honfluer, then a tour of the D day beaches. Also Mont St Michele. After that head south to the Bordeaux area for wine tours/tasting. St Emilion looks like a lovely area to stay in the Bordeaux region? We are hoping to spend some in the Loire as we head south and before arriving in Bordeaux.

I appreciate your thoughts on how best to put this trip together!