Thin insulating films are commonly employed for the electronic decoupling of molecules as they enable a preservation of the intrinsic molecular electronic functionality. Here, the molecular properties of 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA) adsorbed on insulating CaF thin films that were grown on Si(111) surfaces are studied. Scanning tunnelling microscopy is used to compare the properties of PTCDA molecules adsorbed on a partly CaF-covered Si(111) surface with deposition on thicker CaF/CaF/Si(111) films. The identification of mostly single molecules on the CaF/Si(111) interface layer is explained by the presence of atomic-size defects within this layer. Geometry-optimisation calculations using density functional theory reveal a geometry on CaF(111) of nearly flat-lying PTCDA molecules with two oxygen atoms displaced towards calcium surface ions. This geometry is in agreement with the experimental observations.