Leaving a French registered car in Germany

You mean that you want to park your car in a parking garage close to train station and then continue journey by train? In this case I do not see an issue as long as garage supports your needed parking duration.

... and if I leave it parked on the street?

Probably no problem as long as it is legal to leave it parked on the street for the time period you are gone. Sometimes a car can be parked on a street only for a day or two and then it has to move.

Can become a problem when a sudden parking ban is established, e. g. for moving load, tree care or street improvements.

It is expected in Germany that you check a parked car every 3-4 days which is the pre-run time to stand up the interim signs for parking bans. Worst case is that your car is towed away and that you get an expensive ticket. Even worse if you arrive late and your car was towed away to a gated area, e. g. towing company, and that you can get back your car earliest next day.

Do not forget that around train stations also criminals follow up how long a car is parked at the same place.

I think I could risk that, as only away for about 5 days.
I was more worried about the police or customs objecting to there being a foreign registered car in Germany whose owner is not in the country.

OK, finally be aware of parking tickets. In public I am not aware that the machines accept 5 days.

Trick: Try EasyPark app for your planned parking destination and put a printed page with the logo into front window. So every day you can pay remote for parking - if needed.

Thanks MarkK

You also need to make sure that you are not driving into an area where a German environmental sticker is required (unless you somehow have one).

good point about the Umweltplakette, which would pretty much rule out many larger stations.

Sort of like driving and parking a German car near a station in Strasbourg or Paris without a Crit'Air.

I didn't think about the Umweltplakette. Do they maybe let foreign cars get by without one?

My understanding is that enforcement is stricter in Germany than it is in France for Crit'air (where there seems to be nearly no enforcement outside of pollution alert days). I am not sure about what happens in case of a violation: if it is "just" a fine it is OK I guess, but if you have to turn around it is no good!

Do they maybe let foreign cars get by without one?

Strictly no. That was one of the reasons why I was starting with privately operated parking garge.

To stop all the guessing around. Which train station?

Heidelberg or Mannheim

Mannheim has a low emission zone.
Heidelberg had skipped it since March 2023 (article).

Info: Map of German cities with low emission zone.

Free of charge inner city parking in Heidelberg is allowed at Messplatz. From tram station Messplatz you can take line 26 to Hauptbahnhof Süd (main station South entry) [network map] - just 2-3 stations.
If you want to look for closer parking garage options you can use Parkopedia.

Thanks again MarkK!