Looking to drive from Basel Switzerland to France, Germany then back to Basel. Is this allowed with a rental car. Or will public transport be the only option.
If you are arriving at Basel Airport (EuroAirport) then rent on the French side (it will be alot cheaper than the Swiss side); it may be even cheaper if you rent from Freiburg in Germany. Try Autoeurope for a quote.
You are allowed to drive between the three countries but nowadays rental companies will likely add a small premium to do so.
Try making a dummy booking with the pick up and drop off locations and someplace it should tell you which countries you’re allowed to drive in without encountering an additional charge. If not, ask the rental company.
When I rented in Germany, through Costco and Enterprise being the rental company, there were a number of countries I was allowed to take the vehicle into. Conversely, when I rented in Spain, also through Costco and Enterprise, I could only take the vehicle into Portugal, Andorra, and Gibraltar without encountering an additional charge.
You might want to consider taking a train from Basel to Strasbourg, then renting a car there and touring Alsace and continuing into the Black Forest. Then you could head back to Strasbourg, return your car there and train back to Basel.
OR you could rent the car in France and use it to tour Alsace (where it is helpful to have a car) but then return it, and take the train from Strasbourg to the Black Forest. Germany has such a good train system that you really don't need a car there.
It would definitely be cheaper that way, unless of course, you are looking to do some leisurely driving and sightseeing all along the way.
Either way, I concur that AutoEurope is a good start. It's a car rental consolidator so you can get a variety of prices from different companies. I have used AE a lot and have always been happy with them.
When I rented/returned in Zurich, I was warned not to drive in Poland, but I confirmed verbally that I could go to Germany. Today you might want to check for a German environmental sticker on the car - haven't done this lately. They can be bought retail, I think, but probably not at the rental station in Switzerland.
Some other stop ideas:
https://community.ricksteves.com/travel-forum/switzerland/interesting-town-near-swiss-german-border
Be advised that driving in Strasbourg requires a special environmental vignette. It's not expensive and you can get it online.
The Man in Seat 61 posted a video of a train ride along the Rhine that sounds similar to this routing