As a solo traveler who cannot drive a car with a manual transmission, I've never considered renting in Europe. In general, driving will be a lot more costly than taking the train as long as you don't buy your long-distance rail tickets very late in the game--and even then, the car might be more expensive. Now, whether throwing Switzerland into the mix would change that calculation, I do not know. Most people who go to Switzerland dstrong texto so primarily for the scenery, and they want to take one or more high-elevation trips. You can't drive to tops of those mountains; you have to use things like cog-wheel trains, so some of the public-transportation expense would remain even if you had a car.
Parking in a convenient location in one of the popular cities in Europe will not be cheap. Some highways have high tolls. Switzerland is one of the countries that uses a vignette system rather than tolls. There is no short-term vignette, so a tourist on a brief trip pays the same fee as someone living in the country.
Basel and Geneva are two major Swiss cities sitting on the border. You could visit each for a day from a nearby French town without incurring Swiss rail fares or hotel expenses.
I'd apply some of the ex-Swiss time to Paris and add an extra day or two for the Netherlands. If you're interested in art, Rotterdam has an interesting modern-art museum and The Hague has the Mauritshuis. The Kröller-Müller Museum in Otterlo is a place I haven't gotten to yet; not sure how easy it is to reach by public transportation. You might also be interested in the way the Dutch reclaimed areas from the sea to expand their living area.
The Swiss Alps are beautiful. So are the vastly less expensive Italian Dolomites and Austrian Alps (perhaps a bit far afield for you on this trip). I haven't gone up into the French Alps, but from descriptions on this forum, Chamonix has marvelous Alpine scenery and a walk-through-glacier. You can use Alpine lifts to cross the border into Italy.
There are always more places than a traveler can hit on any given trip, whether the limiting factor is time or money. I spent 89 days in France last year, basically just in eastern France. I didn't have time for Paris (or Chamonix). Focus on choosing a collection of destinations that makes sense, given your constraints, not on the hundreds/thousands of great places in Europe you are not going to be able to see on this trip. In other words: I've have no problem setting Switzerland aside.
I doubt very much that you'd save money with a rail pass. It's a very rare traveler who does. Don't forget that many of the fast trains require seat reservations. Rail pass holders pay extra for those, but those fees are included in the point-to-point ticket prices you see online. For example, these are the second-class reservation fees on the Thalys:
Netherlands-Belgium: 15 euros
Netherlands-France: 25 euros
Belgium-France: 20 euros
There may be quotas for rail-pass holders on those trains; I'm not sure about that. Such quotas do exist on some international trains.
Rail fares in Germany can be extremely low because of some great deals on regional tickets.
You could currently buy a June ticket from Annecy to Beaune for 47 euros. I found an evening train from Beaune to Paris going for 15 euros; others were 23 euros, 35 euros, etc. If you're in a position to lock down your major travel legs soon after the tickets go on sale, you'll do far better than with a rail pass. I didn't buy any of my French rail tickets more than a very few days in advance, and I didn't run into exorbitant costs. It helped that I traveled to a lot of smaller towns, which often involved use of regional trains (TERs). Fares on those are relatively inexpensive and do not increase as the date of travel approaches.
