France and Germany, how to arrange our time?

I think the first thing you need to do is review your math. If you only have 10 days, and 5 of those are in Paris, that only leaves 5 days for all of the places you want to see, and completely disregards the travel times between places. Even if the 10 days were in addition to the Paris days you mention, I don't see how it is possible to stay "several" nights in all of those places. I think, unless you can lengthen your trip, you should consider shrinking the number of areas you are trying to cover. Have you spent any time looking at the via Michelin site for driving times and costs between each of these places? It's a good place to start.

Sadly this impossible with only five days after you give five to Paris. Do Paris and Alsace or Paris and Provence. It still will be rushed.

No no, sorry, we have a total of 17 nights, the last 5 of which are in Paris! Actually looking at the calendar again, we have from the 12th to the 23rd elsewhere, with the 24th being our first night in Paris. (The 12th barely counts though as we will probably stay close to Paris if not in Paris, due to our red-eye/early morning arrival.)

In Rothenburg consider staying in this centrally located apartment - www.froehlich-rothenburg.de/en

That looks lovely Stephen. Did you stay there? Is it inside the wall?

In Rothenburg, I can recommend Gasthaus Alter Keller for lodging. They rent several rooms above their very good restaurant (one of the most popular in town). We rented a family room, which consisted of an entry hall with bathroom, then two separate rooms each with two twin beds pushed together. It was perfect for us and our two teens in June 2018. Its over 800 years old, so expect lots of character and slightly sloping floors! It’s just behind the main street behind the square, so very central yet quiet. Parking is a pain in Rothenburg. You can park at the restaurant to check in and drop off bags, but then you park in one of the public lots.

Be sure to get up really early (before 7am) and stroll around the town. The crowds arrive by 10, and it’s magical to experience it in the early morning with just a few others (mostly photographers and locals). The Nightwatchman’s Tour is great and provides some very interesting history.

We also stayed at the Gasthaus Alter Keller, and enjoyed it very much.

First off, are you driving from Paris to Bavaria, and considering driving from Provence back to Paris?

With only ten days, choose two out of your four regions for a more relaxing stay. I stay a minimum of one week in any location and find more than enough to do, in Germany or in France. If Rothenburg is a must, I'd go with 5 nights there. I was once in contact with the lady in the link provided by Stephen, none of her apartments were available for our time period: they are within the city walls. Same with this lady: https://www.gaestehaus-prien.de/

I never stayed here either, but the owners were very helpful to us on a couple of occasions: https://www.hotel-reichskuechenmeister-rothenburg.de/en/home.html They also have apartments now.

From Rothenburg you can hit Wurzburg, Nuremberg (both better visits than Heidelberg); Dinkelsbuhl, Nordlingen (combined); the under visited Schwabisch Hall, lovely Iphofen and Bad Wimpfen (the latter can be combined with a visit to the salt works at Bad Friedrichshall). Close by is an outdoor museum in Bad Windsheim : many Bads usually means good things. Some of these trips are under an hour, the furthest about 1.5 hours. Even if you have a car, it might be better for the four of you to take a train in some instances.

Next, choose Alsace or Provence. I've never been to Provence, but if that's also a must for you then go spend five nights there. I'd choose Alsace, because of the distance. We once spent three weeks based in Riquewihr, and by the end I could order flammerkooosh and showkroot garny like a local.

There's nothing particularly complicated about renting two cars instead of one, and the drive from Alsace to Provence is a long one, prone to traffic around the May holiday weekends. I would take the train between those locations.

And if you drop Alsace altogether (makes sense time-wise!) to focus on S. Germany, a flight from Munich to Marseille could work as well, or I think there is also a train from Frankfurt to Provence, stopping in Mannheim, but it might have been a casualty of Covid.

Yes it is inside the wall, close to the church and marktplatz. I‘ve stayed twice and will again next summer

It's not so much that we "love" trains, it's just that we get there faster with a lot less hassle. I'm sitting in a Vannes to Paris TGV as I write this. If you have taken European high speed trains, then you are familiar with the options. If not, more research is needed. Of your 11 days, four are very long driving days.
Anyway, from Germany, I'd fly to Nice, or preferably Marseille given your interests. Even the train would be long. A car is a waste of your precious vacation time.
Check ViaMichelin.com and the man in seat 61 dot com for info.

Thanks for the ideas. I've reached out to a couple of the places in RodT, hope to get good news from one or the other!

ViaMichelin is great, have been using it for our planning. I love that it gives you not just the distance, but the cost, as well as route choices.

We will drive from Paris to Rothenburg, as the train trip is no shorter from our research on SNCF, or according to Rome2Rio. When you multiply the fare x4, it's no cheaper than a rental car. It doesn't seem to better from Alsace to Provence. Provence to Paris would be easy on train, but that's not enough of a help to give up the round-trip rental. I've done trains in the Netherlands and Hungary, and would love to get the kids on a train, but it's just not going to happen in this trip.

Any thoughts on a home base in Provence for our interests? (I will probably move to the France forum also, as the multi-national research is behind us now.)

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"We want to spend time in Baden Wurttemburg and Bavaria, then get down to Provence.... Interests are Roman sites and Medieval towns"

Bavaria? I don't see much of Bavaria in your trip, and nothing much at all of Rome; neither Bavaria nor Rothenburg is very close to your Paris > Provence trajectory.

Why not explore some historic places in Germany where the Romans actually set foot and that are closer?

Trier (on the Mosel River) itself is a Roman Museum.

The Mosel River has numerous Roman sites:

https://www.worldhistory.org/article/1657/a-roman-trail-in-the-moselle-valley/

In nearby Homburg:

https://www.tripadvisor.com/Attraction_Review-g198476-d7119437-Reviews-Romermuseum_Schwarzenacker-Homburg_Saarland.html

Mainz is an option too:
https://www.mainz-tourismus.com/en/explore-enjoy/living-culture/museums/sanctuary-of-isis-mater-magna/
https://cdn.meine-vrm.de/TiUGkEUyGQUxXij1tpUtMNz-CNk=/1200x628/smart/819%2F18435%2F18435363%2F35420809.jpg

Medieval towns:

Bernkastel (On the Mosel near Trier)

Tübingen

Gengenbach

Schiltach

Strasbourg, Colmar, and Riquewihr just west of the German border in France

Thanks Russ. You're right, we're mostly targetting Baden-Wurttemburg but may dip into Bavaria. Will definitely check out your links, thank you. It was to be a trip to France, actually, but we couldn't resist a little Germany...we got engaged 30-some years ago in Lahr, and in part we're looking for places we visited then, but trying to be open to new places as well. Provence has a ton of Roman sites, of course, so B-W was primarily checking the medieval box...

Where are you getting the info on train fares? May is in a long time; if you book when sales open, you can get tickets from Paris to Strasbourg for 30€ (or even less with Ouigo low-cost trains), and it is almost twice as fast as driving. You could then rent the car in Strasbourg to reach Rothenburg by early afternoon (vs. evening, if you drive from Paris).

You can then drive to Provence if you so desire (not ideal, but the train can be complicated), and take the train back to Paris. In my experience, there is little price difference between a one-way and a round-trip rental within France, as several large rental car companies (I forgot which ones) do not charge drop-off fees.

I totally agree that ten days is hardly enough to cover two of those regions you mention, and there is no way you can do Bavaria, Baden-Württemberg, Alsace and Provence all in ten days. I would leave out either Germany altogether if you want to focus on France, or the Provence as it is the farthest drive.

Rothenburg ob der Tauber, Heidelberg, Freiburg would all require one home base each. I wouldn't want to do any of these as day trips from each other.

either go all Germany or all France

Well, you can do some of Germany and some of France if you choose the adjacent regions. Baden-Württemberg and Alsace would go together nicely. But that would mean leaving out Bavaria and the Provence.