Train from Paris to Trier. Then rent a car. Trier to Black Forest to Lake Constance to Fussen to Munich to Berchtesgaden to Salzburg to Rothenburg to Mainz to Koblenz to Cochem to Kolm to Dusseldorf (fly out) Or Drop Black Forest and Lake Constance and keep everything the same. Or Open to ideas. Must do 3 nights Mosel. Thank you.
I am definitely someone who prefers nature rather than big cities, so if it were me I would definitely do the Lake of Constance. I found it to be amazingly beautiful and would return there (and have a few times) I also love Salzburg and enjoyed Munich. I have been to Koln and Dusseldorf and have no need to return. Not made it to Trier yet (although I am only about 60 miles away right now) but it is on my list and I heard it was great. Some of the experts on Black Forest area will probably chime in... I drove through a number of years ago and stopped at a town or two, but don't remember much more.
Depends on when you're going and how willing you are to do one-night stays, which will be neccessary for a trip spanning this many places. If you're going in the summer, Lake Constance is lovely and well worth a visit for both the charming towns on the lake and biking/swimming/boating opportunities. Mid-October-April you'll find it gray and shrouded in fog. The Black Forest is nice but being from NorCal you aren't going to find it geographically stunning by comparison with say, coastal redwood forests. If there's anything to drop, that would be it. I don't understand training to Trier, then doing this big loop to get back to Cochem. Cochem is about an hour from Trier by train, less if you're driving (I think). Trier, Cochem, Koblenz/Mainz (also not sure if Koblenz is really that worth a stop to be honest with your timeframe) then on to the Black Forest and/or Lake Constance makes more sense. Edit: unless you're using Koblenz as "starting point for a trip down the Rhine" in which case it makes perfect sense. But yeah, you'd be wasting a lot of time to be in Trier and bypass it and loop around to go back to Cochem. Trier-Cochem (3 days Mosel) - Rhine (Koblenz to Mainz) and then if you want to go to the Black Forest, just hop on the A5 from there, or cut over towards Rothenberg and drive down to Fuessen from there.
Why not take the train from Paris into Nurnburg and rent your car there? Then, go NE to Mosel for your three day stop. You can easily work your way south toward Munich and get into your planned circle trip.
I've been to the Black Forest, and done the Rhiine River Valley trip twice out of Amsterdam. When in Germany, I prefer to spend time in Southern Bavaria and around Innsbruck. And Salzburg is just great.