Interface effects on the ferroelectric behavior of PbTiO3 ultrathin films deposited on a SrTiO3 substrate are investigated using an interatomic potential approach with parameters fitted to first-principles calculations. We find that the correlation of atomic displacements across the film-substrate interface is crucial for the stabilization of the ferroelectric state in films a few unit cells thick. We show that the minimum film thickness for the appearance of a spontaneous polarized domain state is not an intrinsic property of the ferroelectric film but depends on the polarizability of the paraelectric substrate. We also observe that the substrate displays an induced polarization with an unusual oscillatory behavior.