The integration of ferromagnetic and ferroelectric materials into hybrid heterostructures yields multifunctional systems with improved or novel functionality. We here report on the structural, electronic and magnetic properties of the ferromagnetic double perovskite Sr2CrReO6, grown as epitaxial thin film onto ferroelectric BaTiO3. As a function of temperature, the crystal-structure of BaTiO3 undergoes phase transitions, which induce qualitative changes in the magnetic anisotropy of the ferromagnet. We observe abrupt changes in the coercive field of up to 1.2T along with resistance changes of up to 6.5%. These results are attributed to the high sensitivity of the double perovskites to mechanical deformation.