https://soziales.hessen.de/Corona/Fr...t-auf-Englisch
This is stating very clearly that in Hessen (state where Frankfurt am Main and FRA airport is) a FFP2 is mandatory in public transport and all other compulsory situations.
Basically, you either wear a FFP2 mask or none at all.
Legally, this is also applying to the FRA airport. Many, many people wear very different types of masks in the airport, including cloth. They are never questioned/warned.

However, as stated before, I've never seen or heard from anyone being questioned or warned why are they wearing a simple surgical mask.