I can see several problems with the early part of your itinerary:
1) The route takes you through Italy. You may not be able to take your French rental car into Italy (last time we rented a car in the South of France Italy was a "no-no")
2) The Stelvio Pass may not be open. It's summer-only, and it officially opens on 1 June. Sometimes mountain passes are open before their official opening date, but it's far from guaranteed.
3) Nice to Davos is over six hours driving time without the Stelvio Pass (and that's Google Time which tends to be somewhat over-optimistic). Driving on mountain passes takes a LONG time. I don't think the trip can be done in a day even if the pass is open. You'd have to drop the pass, and that probably means your whole reason for going to Davos has gone.
I know you want to see a bit of Europe, but Nice to Paris via Davos and Colmar seems an awfully long detour, and all you'll be doing is driving and driving and driving.
Another thing is that it's the Pentecost week-end, which means that the Monday (25th) is a public holiday virtually everywhere in Europe, and with another public holiday (Ascension) only ten days earlier a lot of people will be travelling around that time, so expect roads to be very very busy.
I'd drop Davos (and possibly Colmar too) and take a more leisurely drive on a more direct route - allowing plenty of extra time for the holiday week-end traffic jams.