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 depends on the properties of the rock they are in. Frankian caves are formed inside a rock which is mixed limestone and dolomite. Both react different on chemical solution by water. The result are caves with narrow passages conecting 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 are numerous patches of phantastically eroded dolomite, forming rocks, cliffs, balancing rocks, mushroom rocks, and even structures looking like prehistoric remains and stone circles. So the characteristic of this area are actualy the bizarre rock. Especially the rock with the runied castle in Pottenstein shows this. The rocks of Tüchersfeld even made it on a stamp of the Deutsche Post.