La0.7Ca0.3MnO3 optimally doped epitaxial films were grown on ferroelectric BaTiO3 substrates. Electronic transport (magnetoresistance and electroresistance) and magnetic properties showed important anomalies in the temperature interval between 60 and 150 K, below the metal-insulator transition. Scanning probe microscopy revealed changes in BaTiO3 surface morphology at those temperatures. La0.7Ca0.3MnO3 thickness is a critical factor: 120-angstrom -thick films showed large anomalies sensitive to electric poling of the BaTiO3, whereas the behavior of 150-angstrom -thick films is closer to that of the reference La0.7Ca0.3MnO3 samples grown on SrTiO3. We propose that, through inhomogenous strain and electric polarization effects, the ferroelectric substrate induces an inhomogenous spin distribution in the magnetic layer. This would imply the coexistence of in-plane and out-of-plane ferromagnetic patches in La0.7Ca0.3MnO3, possibly interspersed with antiferromagnetic regions, as it has recently been theoretically predicted. Substrate poling effects are investigated, and a magnetoelectric coupling is demonstrated.