This paper reports on the voltage dependence of the magnetization reversal of a thin amorphous ferromagnetic TbFe film grown on a ferroelectric and piezoelectric BaTiO3 single crystal. Magneto-optical measurements, at macroscopic scale or in a microscope, demonstrate how the ferroelectric BaTiO3 polarisation history influences the properties of the perpendicularly magnetized TbFe film. Unpolarised and twinned regions are obtained when the sample is zero voltage cooled whereas flat and saturated regions are obtained when the sample is voltage cooled through the ferroelectric ordering temperature of the BaTiO3 crystal, as supported by atomic force microscopy experiments. The two steps involved in the TbFe magnetization reversal, namely nucleation and propagation of magnetic domain walls, depend on the polarisation history. Nucleation is associated to coupling through strains with the piezoelectric BaTiO3 crystal and propagation to pinning with the ferroelastic surface patterns visible in the BaTiO3 topography.