FOTO-KOCH E725 FRANKFURT-M. on the back of an old photo. Was photograph taken in Frankfurt or just developed there?
Certainly only developed there. These are markings added during the printing process.
There is usually nothing on a film that tells where the photo was taken (except perhaps on very specialized cameras for aerial survey/recon), and when there is it is on the photo side of the print.
Definitely the lab's doing. Of course, the photograph could also have been taken in Frankfurt, but that has nothing to do with the stamp on the back. My best guess would be that FotoKoch is the lab, E725 is the Contax II Zeiss Ikon (perhaps the lens they used for the enlarger?), or it means "developed in Frankfurt, manually".
Is there a date anywhere on the picture? Would love to see it!