My experience is limited to one recent trip to SW Germany and Eastern France, so others may have a lot more wisdom & experience to share.
That said, it seems that you are simply flying LHR (or Gatwick) to FRA after you will have spent time in England/London. So that is a short flight and you can get a train from the airport in FRA to Mainz and then to Boppard easily enough, assuming you have a morning flight out of London. You can get a train at the airport without going into Frankfurt. Whether you should spend time in Frankfurt is not an issue I can begin to address.
With 3 or 4 days based in Boppard, you can explore the Rhine, perhaps a bit of the Mosel, castles in that vicinity, Koblenz or Mainz, even. Train, boat or biking are all possibilities for some of that.
I think the Black Forest likely deserves more than a day trip. My wife and I were just talking about our jam packed, travel by rental car day in the BF, which was a 24 hour day. We drove into the Black Forest from Tubingen, a couple of hours east of the BF, via Burg Hohenzollern (the Kaisers’ 19th C. restored and re-envisioned castle) and we spent the night in the central BF, near Schiltach. (We unfortunately had to cancel our dinner Rez, since I was sick as a dog that night but bounced back the next morning, thank goodness) The next day we drove to Freiburg with stops at
- Black Forest Open Air Museum
- Triberg
- Ravenna Gorge for a hike
I learned on this forum that there is a town about a 35-40 minutes drive north of Schiltach, Baiersbronn, that is a food lover’s, farm-to-table restaurant delight … but that was the dinner we had to cancel at the last minute.
We chose Freiburg as a place to spend two nights. Glad we did. The historic center was great. Learned a few things and enjoyed what might have been my favorite market of several that I’ve been to in Italy, Austria, Germany, France, Spain and England.
As for cycling through Alsace, there are a number of cycle routes from Colmar that you can and will enjoy to towns like Eguisheim, Turckheim, Ammerschwihr, Kaysersberg and Riquewihr. Easily two days of cycling among those, and you can spend the night between those two days back in Colmar. If you choose, you’ll be able to arrange some wine tasting, as well. See https://www.ruedesvignerons.com/en/region/vignoble-alsace
Colmar deserves some time for the town, sights, dining, shops snd sightseeing. Rick Steves raves about Unterlinden Museum, but we instead enjoyed some music as part of the Journees de Patrimoine the weekend we were there.
Hopefully you will get some wise responses from others, including Russ, KGC and Mardee who have passions and knowledge re the SW Germany pieces of your potential itinerary.
FWIW, our own relevant TRs are at https://community.ricksteves.com/travel-forum/trip-reports/sw-germany-e-france-alsace-burgundy-pt-3-of-4.
From there you can proceed to Part 2 that includes Freiburg and the Black Forest (plus Mainz and Tubingen among other stops) and Part 1 that includes the Mosel, Koblenz and our peek down the Rhine as we cycled Koblenz-Boppard-Marksburg Castle-Koblenz.
Enjoy your planning and your travels.
