Is there a European or German equivalent to the ASMP for professional photographers?

Yes. Europe doesn’t have a single direct equivalent that covers all countries in the same way, but there are national and regional professional organizations.

From the answers provided:

• Association of Photographers (AOP) is a trade association focused mainly on British and European professional photographers, and it also accepts members from other countries.
• In France, a comparable organization is the Syndicat National des Photographes.

For Germany, the answers don’t name a specific organization, but the general point is that professional associations in Europe are often organized at the country level rather than as one EU-wide body. Searching in the local language and looking for national trade groups, unions, or professional associations for photographers is usually the best approach.