Do a search in the AA forum on the FRA AAdmirals Club. If you're not a member, no worries---as an AA Platinum, you'd be able to use it in between your flights. It was THE pitstop for a lot of FRA MR's last winter. It's landside, upstairs from AA's gates, across the catwalk from the Sheraton hotel. (if you're heading out of security & immigration, you could pretty much just follow the signs to the Sheraton hotel that's at the airport, if you start walking across a "catwalk/skybridge" over to a Sheraton hotel, you've gone too far...turn around & its behind you).

Showers (sign up at the desk, first thing when you enter), decent expresso, internet, some basic snacks, and awesome staff that are definitely clued in to mileage running.