I found it here: https://www.dnb.com/utility-pages/dnb-demographic-firmographic-code-tables.html:
There are 2,4,6,8-digit SIC, Local Activity Type, and NAICS.
Here is a link to a dataset of businesses from Paducah, KY, which include a SIC designation.
I'm not exactly sure what's going on with these industry codes. I looked into it briefly and since it's a six-digit code I'm wondering if it's not reflecting the NAICS 2017 revision or some other weird industry code. I didn't name the columns so I'm not sure what ...
https://offeneregister.de provides basic German company information (companies and their officers) collected by OpenCorporates mainly in the period from June 2017 to January 2019, mainly from the Handelsregisterbekanntmachungen and to a lesser extent the Handelsregister (search results listings) for over 5,000,000 companies.