While technologically challenging, the integration of ferroelectric thin films with graphene spintronics potentially allows the realization of highly efficient, electrically tunable, nonvolatile memories through control of the interfacial spin-orbit driven interaction occurring at graphene/Co interfaces deposited on heavy metal supports. Here, the integration of ferroelectric Hf_0.5Zr_0.5O₂ on graphene/Co/heavy metal epitaxial stacks is investigated via the implementation of several nucleation methods in atomic layer deposition. By employing in situ Al₂O₃ as a nucleation layer sandwiched between Hf_0.5Zr_0.5O₂ and graphene, the Hf_0.5Zr_0.5O₂ demonstrates a remanent polarization (2Pr) of 19.2 μC/cm². Using an ex situ, naturally oxidized sputtered Ta layer for nucleation, we could control 2Pr via the interlayer thickness, reaching maximum values of 28 μC/cm² with low coercive fields. Magnetic hysteresis measurements taken before and after atomic layer deposition show strong perpendicular magnetic anisotropy, with minimal deviations in the magnetization reversal pathways due to the Hf_0.5Zr_0.5O₂ deposition process, thus pointing to a good preservation of the magnetic stack including single-layer graphene. X-ray diffraction measurements further confirm that the high-quality interfaces demonstrated in the stack remain unperturbed by the ferroelectric deposition and anneal. The proposed graphene-based ferroelectric/magnetic structures offer the strong advantages of ferroelectricity and ferromagnetism at room temperature, enabling the development of novel magneto-electric and nonvolatile in-memory spin-orbit logic architectures with low power switching.