15 days days driving in France from Switzerland

How about flying into Geneva, then take train to Lausanne/Montreux, then go back to Geneva and rent the car, do the road trip and return to Geneva for flight home.
I am not well versed in the train routes in France, so some of the driving could possible be reduced. But you won't need it in Switzerland. Don't go to BO for only two nights.

You don't need a car in Switzerland, because of the incredible efficiency of the Swiss train system, and many town are pedestrian only. Also, it's very expensive to take a car across borders, so if you need a car in France, rent and return the car in France.
And I agree, you need more time in the Berner Oberland. Why go to Switzerland and not go to the Alps?
Have a great trip.

Two nights is a very short visit to Lyon, a large, sight-rich city. It's also very short for Colmar and Strasbourg. Two nights is only one day and some odd hours. Most folks who go to Alsace want to see a few of the little wine villages in addition to Colmar and/or Strasbourg--both of which are worthwhile.

Driving into places the size of Strasbourg and Lyon, and dealing with parking, could be quite a challenge and somewhat time-consuming (an issue with such short stays).

I'd drop either Lyon or Alsace and consolidate that time into one destination. I like Alsace a lot, and it's an area where having a car is handy, but it's the outlier here, though the distance isn't great.

I really appreciate the advice. I agree that cars in cities are a drag..... but its so fun exploring little unreachable towns and villages, something that renting a car encourages and often requires more time allowance. With that said, I agree that I need to shorten the distances traveled.

The first part of our 2018 trip was similar to your plans. We flew LHR to Geneva, rented a car (Europecar through AutoEurope) on the FRENCH side of the airport. Drove to Lauterbrunnen for 4 nights (3 would have been enough but we added a night in case of bad weather), then went to Chamonix for l night and Annecy for 1 night . If we were doing this again, we would have stayed 2 nights in Annecy and visited Chamonix as a day trip - Chamonix is a typical ski town, Annecy oozes charm. The rest of our itinerary was different from yours - we returned the car in Sarlat.

but its so fun exploring little unreachable towns and villages

There aren't really any unreachable towns and villages in Switzerland. Unless you're driving of course, then there are several towns and villages where you can't go.

I appreciate all the help. I'm thinking of adding a second night in Annecy (as suggested by Cynthia) and day trip to Chamonix from there. Since we will have a car, We're hoping to find a nice/safe neighborhood in Lyon (2 nights) that's has good public transport for visiting the heart of the city. We decided not to go as far north to Colmar and Strasbourg. If we don't go to the Bernese Oberland, we're considering, on our way back to Switzerland, to explore the area between Besancon and Geneva. We would then return the car and take trains to the Lusanne and Montreal. This trip is still in its planning phase so any other insights are welcomed.

I used to live in Lausanne for a couple of years and know all of your destinations by car and train. It was smart to drop Alsace -- save that for another trip. Switzerland is indeed very reachable by train for all the places you cited. There are some places reachable primarily by car, but you won't need to go there. Weather in late May generally means that snow is still lingering in the higher elevations -- not an issue for a cable car ride but some hiking would be precluded.

Lyon is often best reached by train, but getting into Lyon by car is pretty doable. However, it is a park once situation and then walk or use public transport. I've stayed once across the river in Part-Dieu and two other times in Presque-ile/Old Town. Note if you rent a car for your entire journey from the French side, make sure you have the vignette (highway pass sticker for Switzerland).

One thing about Switzerland is that you have to buy an vehicle permit to bring a car into the country. About 45 USD. I suspect that a car rented in Geneva would already have the sticker. This is worth calling the rental agency about.

It is called a vignette and costs CHF 40. The sticker 2023 is valid from 1 December 2022 to 31 January 2024. If you are coming to Switzerland from abroad, you can buy the motorway vignette at customs as you enter the country.

When you make your hotel reservations make sure you find IF they have parking and what the cost is. In beautiful medieval towns parking is either impossible or very expensive.

Get one of those cardboard clocks sold in Tobacco shops as some towns require them