Since its birth in the 1990s, semiconductor spintronics has suffered from poor compatibility with ferromagnets as sources of spin. While the broken inversion symmetry of some semiconductors may alternatively allow for spin-charge interconversion, its control by electric fields is volatile. Ferroelectric Rashba semiconductors stand as appealing materials unifying semiconductivity, large spin-orbit coupling, and non-volatility endowed by ferroelectricity. However, their potential for spintronics has been little explored. Here, we demonstrate the non-volatile, ferroelectric control of spin-to-charge conversion at room temperature in epitaxial GeTe films. We show that ferroelectric switching by electrical gating is possible in GeTe despite its high carrier density. We reveal a spin-to-charge conversion as effective as in Pt, but whose sign is controlled by the orientation of the ferroelectric polarization. The comparison between theoretical and experimental data suggests that spin Hall effect plays a major role for switchable conversion. These results open a route towards devices combining spin-based logic and memory integrated into a silicon-compatible material.