What is your exact itinerary, including flight numbers, and ticketing carrier?
If flying SkyTeam you should have access to any SkyTeam lounge as your DM status makes you SkyTeam Elite +. There are some complications with FRA's terminals and areas and with who exactly your carrier is regarding third-party contract lounge access. Delta no longer provides this for STE+, only for business class. But if you are flying on KLM/AF metal as a Delta GM+, even on Delta ticket stock, you typically get access to their third party lounges in the event that a ST-run lounge is not available.
There are lots of people on here who are happy to look at your flights, terminals, and status and tell you exactly what the best choice is, but we do need detailed information.
However, keep in mind being Lufthansa's primary hub, FRA is a terrible airport for SkyTeam lounging.