This is based on juicy airfare in hand, so cannot change to Open jaw. We are traveling by train only for the most part, avoiding one night stands. I'm not totally sold on Beaune as the stop between Gimmelwald and Paris, as the train routing is somewhat tortuous from Switzerland. All of the other cities offer good connections and plenty of possibilities for day trips out of the base city.
Day 1 Arrive FRA, Train to Bacharach, Stay Bacharach
Day 2 Stay Bacharach, Day Trips
Day 3 Train to Freiburg, Stay Freiburg
Day 4 Stay Freiburg, Day Trips
Day 5 Train to Interlaken, Gimmelwald, Stay Gimmelwald
Day 6 Stay Gimmelwald, Day Trips
Day 7 Stay Gimmelwald, Day Trips
Day 8 Train to Beaune, Stay Beaune
Day 9 Stay Beaune, Day Trips
Day 10 Train to Paris, Stay Paris
Day 11 Stay Paris, Day Trips
Day 12 Stay Paris, Day Trips
Day 13 Stay Paris, Day Trips
Day 14 Train to Mainz, Stay Mainz
Day 15 Train to FRA Airport