Oneworld Lounges in FRA
The CX and BA lounges are in the other terminal, and if your AA flight isn't leaving from that side, it's about a 20 minute walk/ride to get over there. Not worth it.
BA -- Absolutely dingiest most unappealing lounge ever. It's in the basement, serves the minimum cookies and crackers, and smells funny. Avoid at all costs.
CX -- Not much better than the Admiral's Club, which I prefer because the service is significantly better. Showers are dodgy, the decor is circa 1970s chain hotel, and the food is nothing to write home about.
Your best bet is to stay in the Admiral's Club until you have to get up, go through security, and spend your time browsing at the shopping (just okay IMHO).
Enjoy.