Integrating large amounts of variable renewable power generation increases the need for flexible resources in the power system. Hydropower can be a precious asset for managing the variability in the grid. However, it will be subject to evolving constraints related to changes in the water resources and the operation of multi-purpose reservoirs. This study explores the value of coupling a power system model with a hydrological model that represents the operation of hydroelectric dams, to simulate an hourly hydropower schedule consistent with a realistic management of the hydropower reservoirs at the national grid level. We model the French power system with the optimization model EOLES-Dispatch and assess the impact of the coupling with the ORCHIDEE model, which represents hydropower management. We find that this new method allows us to simulate a hydropower schedule closer to the observed production, while power system models tend to overestimate the flexibility of hydropower. Considering a prospective 2050 power mix, we also find that accounting for these additional constraints leads to more frequent unsatisfied demand, which is underestimated by the usual representation of hydropower. Such a coupling of hydrological and power system modeling paves the way for a more robust representation of power dispatch in future power mixes, taking into account the joint evolution of water resources and power systems.