I agree that it will be more expensive to to drive. You might want to find a place to turn your rental car in before you cross over into Switzerland, then take the train to Geneva and decide if you need a car there. And really, as the others have said, a week is not very long to enjoy all the places between, even if you leave Frankfurt right away.
But if you do want to continue with your plans, I would suggest stopping in the Black Forest and visiting some of the more quaint towns there like Gengenbach (my personal favorite), Schiltach, possibly Freiburg im Breisgau. Unless you really want to buy a cuckoo clock, I would skip Triberg as it gets very crowded and touristed, and Titisee can be a bit touristy as well. It does have a lovely lake, but you will have plenty of opportunities to see gorgeous lakes as you head into Switzerland. The charm of the Black Forest, imo, lies in its small villages and towns.
The Vogtsbauernhof (Open-air Folk Museum) is a wonderful must-see museum that is located outside of Gutach (near Gengenbach) where you walk through on a self-guided tour showing authentic and historic farms of how people lived and worked in the Black Forest up to 600 years ago. I absolutely loved it! https://www.vogtsbauernhof.de/en/visit