For what it's worth, FRA also has public access showers in both the pre-security and in-transit areas of Terminal 1. I randomly came across the pre-security location one day. They're not particularly obvious (near a restroom down a longer corridor by the shopping area), and I didn't try to go in. But based on the style and condition restroom, I'd say they were probably private, but offering little more than running water, soap, and a towel for a nominal fee.