11 day in France, Fly in Paris, out from Nice

I would leave the car behind and travel by train.
Paris (4)
Lyon (2)
Avignon/Arles (3)
Nice (2)

Take the TGV to Bordeaux and get a car there. Travel East through St. Emilion, The Dordogne, Carcassonne and Provence, plenty of "charming beautiful villages, locale food, sceneries" in those areas. I made that drive and wish I had spent more time along the way. Occasionally set the GPS to avoid toll roads if you want a scenic route with lots of small villages.

We did this route a few years ago:
All by train except Normandie

Nice
Avignon
Paris
Bayeux in Normadie (rented car in Paris)
London (droped car off in Paris, Eurostar to London)

If you are visiting Monet's garden at Giverny as a day trip from Paris, it's easy to take the train from Paris Gare St. Lazare to Vernon, 45 minutes, direct morning departures at 8:15 or 10:15 most days (different on Sunday), then 15 minutes by local shuttle bus.

We did a day trip from Paris to Monet's gardens by train on our own many years ago, and it was quite easy. As to the rest of your trip, I'd suggest taking the train from Paris to a place where you can rent a car and go from there. The suggestion of Bordeaux is a good one. Alternatives are the Loire Valley or northern Burgundy.

I would take the train from Paris to maybe Nimes or Montpellier and first explore the Langedoc - maybe even see one of the Cathar castles then head towards Provence before eventually dropping your car in Nice.

I've been twice to Cotignac, which is about a 90 minute drive from Aix and another 90 minutes to Nice. It's a charming small village with lots to do. I loved driving up to Moustiers Saint-Marie and seeing the Gorges du Verdon.

With 11 days you could even do 3 stops on a trip like this.

Giverny, is easy to see on your own from Paris. I do recommend the 8:20 train, and then get an open ticket for your return so that you can stay as long as you need.

Should we head back to Paris from Monet and pick up a train to our next stop, or should we just pick up a train from Monet? We will be going south for sure. Is night train better or early morning? What do you prefer veteran travelers?

Timing wise, I'm not sure it's realistic to go to Giverny from Paris, see Monet's gardens, then head out to wherever you plan to make your first stop. So the question then becomes whether to spend the night in Giverny and head off in the morning or return to Paris and spend the night before taking off by train. In that case, since almost all east-west trains go through Paris anyway, it would make sense to start from Paris. All of this assumes that there are no night trains you can take. I was under the impression that most of them have been phased out,

Timing wise, I'm not sure it's realistic to go to Giverny from Paris, see Monet's gardens, then head out to wherever you plan to make your first stop.

If you get to Giverny by say 10 am and spend say 6 hrs - you can still travel at least 2 hrs and reach a new destination that same evening in time to settle in new hotel & have a nice dinner.

Clueless why you think that is not realistic

I think we will be taking a TGV when we leave Paris to the next town and pick up a car from there to continue to going South heading to Provence region eventually to Nice, catching flight home (no need to spend time in Nice as we have visited twice). My question now is where should we pick up the car, so to see most with our time.

Colmar
Annecy
Avignon

If we go straight to Annecy, did we miss anything that we should see in Colmar and between Colmar to Annecy area?

Thanks bunches!!

If you get to Giverny by say 10 am and spend say 6 hrs - you can still travel at least 2 hrs and reach a new destination that same evening in time to settle in new hotel & have a nice dinner.
Clueless why you think that is not realistic

First of all, getting to Giverny by 10 from Paris may not be practical. But more importantly, getting from Giverny by train to most, if not all, of the places suggested by people here will probably take at least 5-6 hours.