Honeymoon (France + Switzerland)

Really cannot offer much advise on your plan.
Couple of quick thoughts though...
3 nights in Paris if you have not been is probably at least one day too few.
If Colmar is out of your way, look at Annecy ; similar looking beautiful town that is on your way between Provence and Chamonix.
(not the same timbered buildings or German feel but similar canals, flowers everywhere and overall more beauty most say)

Provence is a large area, Nice is technically in Provence so not sure where you are staying but imagine you are thinking Avignon or Aix-en-provence area. Nice is of course part of what they call the Cote D'Azur but that whole area is still also called Provence.

As for dropping off the car, it seems your plan requires you to do so in Chamonix.
I believe I read that only Europcar (which is a good company) has an office there so you will have to use them to rent leaving Paris and returning later to Chamonix.

Always a challenge deciding what to see and sometimes more importantly what you are ok not seeing to make a plan that works well and as you stated are not moving bases every day.

You don't want to pick up a car on your last day in Paris, but on the morning you are leaving Paris. You don't want to pay for overnight parking.
If you want to drive, you can drop the car at the Geneva airport in a special section for French cars that doesn't incur a surcharge.

Uncharacteristically (for me), I am going to suggest zig-zagging to take advantage of trains.

Paris > Provence by train (3 hrs)
Provence > Burgundy by train (3 hrs)
Burgundy > Chamonix by car (4 hrs)

The drive from Arles to Chamonix would probably take you 6 hours or so.

Add one day to Paris and another to any of these destinations.

You'd probably want a car in Provence. Rent one there and return it at the train; rent another in Burgundy and return it in Chamonix.

Have a great trip.

We always take a train to our first destination. Our first trip to France, we were in Paris for a night and the following day we took a train to Colmar. There is a Europcar in Colmar. We took a city bus from the train station to the airport where Europcar is located. We very much liked the little wine villages of Alsace. We drove from Alsace (actually we spent one night in Colmar and two in Eguisheim) and drove to Burgundy which was a pretty uneventful drive.
Are you spending time in Switzerland after Montreux? If so, I think I'd would get rid of the car in Chamonix. The Swiss train system is pretty amazing and a car I think just complicates life.

Thanks for all the suggestions.

I guess I will drop Colmar to add one more night in Paris, and another in Nice.

I now understand Provence is a really huge area. Besides Arles, Avignon and Aix, where else will be recommended?

As for the train and car combo, will definitely consider!

Oops. Forgot that you'd need a Swiss vignette, (permission to drive on the Swiss autoroute sticker), if you took the car over the border into Switzerland and wanted to use the freeway instead of secondary roads. Sometimes there's already one on the windshield of a rental, sometimes you have to pay for one as you cross the border. I don't know the price of a vignette, but this might figure into your decision about driving vs trains going into Switzerland.

A Swiss Autobahn Vignette costs CHF 40 for 1 calender year (2018). It is a toll for using the Autobahns/Autoroutes/Autostrada.
French Autoroutes have the standard method of charging tolls by distance.

If you restrict yourself to non-Autobahn roads you do not need a Vignette, but that would be restricting, and you would have to get off the French autoroute before the border and cross the border on a non-Autobahn road.

As far as I can see (assuming you drop your car in Chamonix), you wont be driving in Switzerland.
If you can't drop off the car in Chamonix, another option is the French side of Geneva airport. Good train connections from there to the rest of Switzerland.