We report the observation between 40 and 120 K of anomalous magnetic hysteresis loops in thin epitaxial films of La0.7Ca0.3MnO3 grown on ferroelectric BaTiO3. These hysteresis loops display extremely unusual features: after switching at coercivity, the magnetization overshoots the eventual high-field value. We study the strains in the film and substrate with x-ray diffraction and propose a model of two magnetic moment populations with different magnetoelastic anisotropies. The relative weights of both populations can be estimated by comparison with twin samples of La0.7Ca0.3MnO3 films on nonferroelectric SrTiO3. We propose that the observed magnetization overshoots the result from differences in the magnetostriction balance as the applied magnetic field increases. The picture of a nonuniform strain field in La0.7Ca0.3MnO3 on BaTiO3, caused by the corrugation of the ferroelectric domains in the rhombohedric phase of BaTiO3, is compatible with the magnetic granular behavior observed in the temperature and field dependences of the magnetization as well as in the low temperature magnetoresistance exhibited by the epitaxial film.