Unconventional superconductivity typically emerges out of a strongly correlated normal state, manifesting as a Fermi liquid with highly enhanced effective mass or a strange metal with T-linear resistivity in the zero-temperature limit. In Ruddlesden-Popper bilayer nickelates R3Ni2O7, superconductivity with a critical temperature (T_c) exceeding 80 and 40 K has been respectively realised in bulk crystals under high pressure and thin films under compressive strain. These advancements create new materials platforms to study the nature of high-T_c superconductivity, calling for the characterisation of fundamental normal-state and superconducting parameters therein. Here we report detailed magnetotransport experiments on superconducting La2PrNi2O7 (LPNO) thin films under pulsed magnetic fields up to 64 T and access the normal-state behaviour over a wide temperature range between 1.5 and 300 K. We find that the normal state of LPNO exhibits the hallmarks of Fermi liquid transport, including T^2 temperature dependence of resistivity and Hall angle, and H^2 magnetoresistance obeying Kohler scaling. Using the empirical Kadowaki-Woods ratio relating the transport coefficient and electronic specific heat, we estimate a quasiparticle effective mass m*/m_e ≃10 in LPNO, thereby revealing the highly renormalized Fermi liquid state which hosts the high-temperature nickelate superconductivity. Our results demonstrate that LPNO follows the same T_c/T_F scaling observed across a wide variety of strongly correlated superconductors and provide crucial constraints for a viable model for superconductivity in bilayer nickelates.