Is this Road Trip Too Ambitious?

We are doing a France driving trip this spring. We start in Amsterdam and end in Basel. We’ll be taking a train to Angers from Brussels, picking up a rental car for a week in the Loire, then to Mt Blanc/French alps for three nights and ending in Beaune area for three nights. We will drop off the car at the Dijon station to get a train to Basel. We are allowing several nights in Chamonix for a better chance for good weather to ride the lifts.
It is very expensive to leave a car in a different country and Switzerland requires a permit to drive a French rental car. Switzerland is easy to visit by train with a Swiss Pass that includes lifts. We’ve done several road-trips in Provence but never the Piedmont. Provence is easy to navigate. We find that if Michelin or Mapquest says trip is three hours, we count on at least five or six!

You can count "nights" if you want, but if you're honest with yourself, most of us spend most of every night sleeping...it's the days that are useful for sightseeing, activities, and enjoying a place. Sure, you gotta sleep, so counting "nights" is useful for estimating hotel costs. But you're probably no going for the hotels. You go to see and do things...during the daytime. So count your days. And remember, every time you pick up and move to the next place, that's going to consume much of your day - the mundane logistics.

Rule of Thumb: X nights gets you (X-1) days. As they say, Do The math... Subtract 1 (one) from every number on your list. That's how many usable days you will have to spend enjoying that place. So you get:

Provence: 2 days
Nice: 2 days
Piedmont: 1 day
Turin: 0 days
Chamonix: 0 days
Interlaken/Lauterbrunnen Valley: 1 day
Zurich: 0 days

Looks a little different like that, eh?

13 days is about right for Provence, visiting the Rhône end and the Riviera end, about 6 days each.

Confident driver or not, review the European road sign convention, especially what the red circle means, the no passing sign, and the one that indicates that oncoming traffic has priority.

Don’t rent a car on your day of arrival instead sleep in Marseille and rent a car the next day. I’m sure you’ll get very little sleep if any flying from the states. As already mentioned, the cost of picking up a car in one country and dropping it off in another is exorbitant. Italy also has ZTL zones you need to read up on. Driving in a bus lane could be costly and it only takes a few seconds.
This itinerary is way too ambitious and you’ll spend all your time in a car. I wouldn’t want to drive in Turin either. Why not stay in FR the whole time so you have time to see and experience the south of FR? Slow down and visit IT another time and the same with CH. Besides, you need five nights to see the Lauterbrunnen Valley not two.