Driving between France and Germany and Switzerland one week June 2017

Not sure about your timings. You say pick up car Belfort 2nd June, return it also in Belfort 9th June. That is 8days/7 nights.
But you then say 4 nights Colmar and 3 in Belfort, 4+3 = 7. So you have no nights anywhere else. That restricts you to day trips from Colmar or Belfort.
I can only find one Buix in Switzerland, it is in Canton Jura, near Porrentruy and the French border, so easy trip from Colmar or Belfort.
Crossing borders is no problem. France/Germany is just a sign (both are in EU and Schengen). France/Switzerland is no passports (Schengen), but customs (Switzerland not EU). Most minor roads have spot checks only, they aren't interested in normal travellers, just goods vehicles. If you see somebody, slow down and they will wave you on.

I would recommend Strasbourg as a train day trip from Colmar. Easier than by car.
For wine, there is the "Route de vin d'Alsace": http://www.alsace-wine-route.com/ Lots of pretty villages.

Do you mean "Freiburg im Breisgau" (Germany, near the French border), or the Freiburg in Switzerland (Town+canton), or some other Freiburg? Freiburg im Breisgau is a nice city, worth a day. Swiss Freiburg is nice, as are so many towns.

If you want to drive on an Autobahn/Autoroute/Motorway in Switzerland you need to buy a "Vignette" toll-sticker, cost CHF 40. If you cross the border on an Autobahn, you can buy one there. If you cross on a normal road, you need to buy one (Fuel station) before going on an Autobahn.

You may want to drive to the Alps. That would be a LONG day trip.

Did you look in to a one way rental ?
Strasbourg > Freiburg > Belfort > Dijon > Lyon

Make sure you have a good GPS. That just makes driving easier. Also, know that tolls on French highways are very expensive so plan for that or try to take roads off of major highways, and make sure you stop near the border of Switzerland to buy a Vignette sticker to display on your vehicle. They use the sticker fee instead of tolls. Also, familiarize yourself with road symbols so you will understand the meaning of the road signs.

I plan on using the GPS on my phone. I have service with T-mobile. Do you think that will be sufficient?

Freiburg im Breisgau and the Black Forest is an easy day trip from Colmar. Our GPS got us in and out of Freiburg easily. To sample the local specialty of Schwarzwälder Kirschtorte, a local recommended Cafe Diva in Hinterzarten. It is a lovely high-end setting, and is expensive for cake but a great experience. The Hexenlochmühle (witches den mill) is a tourist trap, but the road winds you into the deepest of the forest and provides a sense of why it is called the Black Forest. This can be done in a day.

Strasbourg has a park and tram combination ticket outlined in the RS book. The lot is easy access from the highway and saves the headache of driving and parking in the inner city.

RS Book adequately describes the wine villages around Colmar. Pick a couple and enjoy a the day. Haute Königsberg is nearby if you have a clear day and want to do a castle with a great view.

It is a wonderful area. Allow time to enjoy Colmar itself, too.

The 40 euro sticker for Swiss autobahn travel is checked if you enter on a highway. If you stay off the highways, it is not needed.

I would point out that Strasbourg is not next door to Freiburg. Check into whether you might need an Umweltplakett for the German towns/cities, especially since you are renting in France. Tell the rental desk every country you are going to before they print the contract. There are too many wineries to mention. The big names can require reservations, perhaps made by your hotel if you learn a name after arrival.

I am sorry we missed Le Corbusier's chapel in Ronchamp. Basel is a big city, but has lots to see. Besancon may be too far for you, but we enjoyed the hilltop citadel. If you are actually going to Lyon, I would much rather go to Perouges-it is a must-see. Are you making advance dining reservations for any Michelin three-stars? We found L'Auberge de L'Ill (that's the name of a river, I-L-L) to be an exceptional experience, must book in advance.

One important point to note is that each driver listed on the rental form will require an International Driver's Permit, which is used in conjunction with your home D.L. These are easily obtained at any AAA / CAA office for a small fee and are valid for one year. The other option to an IDP is a certified translation in French of the terms of your license.

http://franceintheus.org/spip.php?article376

I stayed in tiny Eguisheim, just the other side of the highway from Colmar. It was perfect. I was just a couple minutes' drive from the highway to visit the sights and villages but didn't have to drive in and out of Colmar (a sizable city) and contend with its traffic (and pay for parking). There are other larger villages nearby to choose from. There are good restaurants in all the villages (the tourist industry is very well developed), so you can park the car after a day's sightseeing, walk to dinner and drink the local wines without having to drive home afterward.

Roads in Alsace are quite good, but except for highway, they are two-lane and without shoulders. I had no trouble driving on them. Seems to me that the highway south of Colmar is tollway, but the section from there to Strasbourg is free. Places I enjoyed there -
Day 1 - Riquewihr, Hunawihr, Ribeauvillé (villages), Haut Koenigsbourg (ruined castle), nearby Monkey Mountain
Day 2 - Niedermorschwihr, Turckheim, Kayserberg, Kientzheim (and its wine museum )

Strasbourg isn't hard to drive in but it can be slow because of the traffic. And you'll pay for parking.

Things to know about driving (in France, don't know about Germany). First, there's lots to know. Speed limits on the highways are enforced by radar and cameras. If you are even a little over the limit, you may get a ticket. Speed limits are lower when it rains. Off the highways, speed limits aren't always posted but you are expected to know them (and all the other rules of the road in France). There are some radar/cameras on the roads, so be careful. The locals will speed (my guess - they know where the speed traps are) so just let them pass you. Tickets are expensive. You need an International Driving Permit (IDP) for each driver. You may never be asked for it, but if you are and don't have it, it's could be a costly problem. You can get them for about $20 each at AAA. Blood alcohol levels are lower 0.5% than in the U.S. (0.8%) and taken seriously.

You may need a vignette to drive in Switzerland - in essence they charge a flat fee for driving on the roads instead of having toll roads. I think it's only required on the highways, so if you are taking a local road, you may not need it. You need to find out - and where to get one if you do need it. viamichelin.com is a good site to find driving routes and estimate driving times. It will calculate the cost and will probably figure out if you need the vignette.