The remarkable ability of phase change materials (PCM) to switch between amorphous and crystalline states on a nanosecond time scale could provide new opportunities for graphene engineering. We have used density functional calculations to investigate the structures and electronic properties of heterostructures of thin amorphous and crystalline films of the PCM GeTe (16 Å thick) and Ge2Sb2Te5 (20 Å) between graphene layers. The interaction between graphene and PCM is very weak, charge transfer is negligible, and the structures of the chalcogenide films differ little from those of bulk phases. A crystalline GeTe (111) layer induces a band gap opening of 80 meV at the Dirac point. This effect is absent for the amorphous film, but the Fermi energy shifts down along the Dirac cone by -60 meV. Ge2Sb2Te5 shows similar features, although inherent disorder in the crystalline rocksalt structure reduces the contrast in band structure from that in the amorphous structure. These features originate in charge polarization within the crystalline films, which show electromechanical response (piezoelectricity) upon compression, and show that the electronic properties of graphene structures can be tuned by inducing ultrafast structural transitions within the chalcogenide layers. Graphene can also be used to manipulate the structural state of the PCM layer and its electronic and optical properties.