Check it out on
AIRPORT Flughafen Flugplatz Pilot ( www . airports . de )
I have a very vague memory of very early closing hours, better ask if you do call them. Which is ALWAYS a good idea, often even mandatory for PPR.
BTW Baden-Baden means "the city of Baden in the region (or county, or whatever) of Baden". Today that region is joined in the state of Baden-Württemberg.