The Frankian Jura, similar to the Swabian Jura, is part of the South German Scarplands. The geologic structure, the kind of Mesozoic rock layers it is composed of is almost identical. So please have a look at the Swabian Jura page for more details on the geology.
The upper layer of the high plateau in Frankia is also Malm, Upper Jurassic, but here it is a little thinner, and it is composed mostly of dolomite, a different variety of limestone. The difference is the chemical composition, limestone is pure CaCO3, in dolomite most of it is replaced by the chemicially similar salt CaMg(CO3)2 ersetzt. The dolomite was named after the French geologist Déodat de Dolomieu, who also gave his name to the mountain range and the Italian/Austrian border. You guessed it: those mountains are composed of the same rock.
The structure and character of caves depend on the properties of the rock they are in. Frankian caves are formed inside a rock which is a mix of limestone and dolomite. Both react different on the chemical dissolution by water. The results are caves with narrow passages connecting frequent huge chambers. Only a few caves show almost constant size, similar to Swabian caves, and those are located in small areas of pure limestone, e.g. Bing Cave (Streitberg Cave) in Streitberg.
A very characteristic and romantic result of the geology is frequent patches of fantastically eroded dolomite, forming rocks, cliffs, balancing rocks, mushroom rocks, and even structures looking like prehistoric remains and stone circles. So the characteristics of this area are actually the bizarre rock formations. Especially the rock with the ruined castle in Pottenstein shows this. The rocks of Tüchersfeld even made it on a stamp of the Deutsche Post.