We introduce superlattices made of ferroelectric halide perovskites as a class of functional materials possessing large Rashba effect and phase transition from normal insulator (NI) to topological insulator (TI) induced by an electric field. Using first-principles methods, in $\mathrm{CsPb}{\mathrm{I}}_{3}/\mathrm{CsSi}{\mathrm{I}}_{3}$ and $\mathrm{CsSn}{\mathrm{I}}_{3}/\mathrm{CsSi}{\mathrm{I}}_{3}$ superlattices, we found a nonmonotonic Rashba parameter with respect to the magnitude of polarization and large maximal Rashba effect at a critical polarization, where the phase transition from NI to TI occurs when changing the polarization. This phase transition and the large maximal Rashba effect are related to band-gap engineering under an electric field. In contrast to traditional nonpolar TIs, in these ferroelectric TIs, the energy level of the Dirac point and the spin texture of surface states are largely tunable by changing polarization or strain. Our results thus highlight the interplay among ferroelectricity, Rashba effect, and topological order in a single material, which is promising toward electronic and spintronic applications.