Who are the Uber type transportation companies that are reliable along the Rhine River area of Germany and France?
Good question. Not sure what the answer is - I've always relied on the local transport system for my needs there.
Which part of the Rhine River do you mean, exactly?
The Upper Middle Rhine Valley is the place most tourists want to see, but the Rhine is of course much longer than the little snippet you see in dark green at the link. Where are you headed?
Within the UMRV, I usually stay somewhere inside the VRM zone... train and bus services are intense in this area. And some towns/lodging establishments issue passes for free use of both.
Uber is available in Koblenz and Frankfurt (especially Uber X), and they are allowing taxi-drivers to integrate their services into the Uber app in other cities so that you can book a regular taxi through the app in other places. I think however you would be better off using trains and buses, and to a limited extent taxis, anywhere in the middle Rhine gorge, as Uber is not really a big thing in rural areas and villages such as you will find along the Rhine. Remember that Uber is a US import and not widespread everywhere else.
Lavandula
The answer might be here:
https://www.uber.com/global/en/r/germany/cities/
And.
Shanah Tovah U'Metukah