Chancy-Pougny is a run-of-river dam on the Swiss–French border constructed in the early 1920s. Since its commissioning, the operation of the four spillway gates has been responsible for a progressive erosion of the stilling basin. The future scour potential of the unlined stilling basin of the Chancy-Pougny dam was assessed by hybrid modeling, combining both a physical and a numerical model. The physical model investigated the flow structure in the basin as well as the dynamic pressure fluctuations exerted by the flow on the rocky bottom of the stilling basin. The presence of a large gyre, generated by a flow recirculation in the nonsymmetrical basin, was found to be one of the main causes of significant scour formation. The numerical model used the pressure recordings to reconstitute the observed scour since 1924, predicting significant additional long-term erosion in the stilling basin. As such, a series of scour mitigation measures, including a free-standing wall and various configurations of concrete prisms for scour protection, were tested on both models. A tailor-made solution containing a layer of randomly distributed concrete prisms laid on the basin’s current bottom was identified through this study, proving the importance of both numerical and physical approaches in hydraulic engineering.