The increasing share of intermittent sources of energy will increase the need for frequency-control reserves. However, the supply from gas- and coal-fired power plants might decrease in the following years. Hydropower technologies are often put forward as mature and low-carbon technologies able to contribute to cover this increasing need for reserves. The procurement of reserves being mostly market-based in Europe, the market design should send price signals to encourage the participation in these markets. This paper analyses the incentives provided by the French market design for seasonal storage and pumped storage hydropower plants to participate in reserve markets. To that end, a deterministic mixed-integer linear optimization model is presented. The objective is to maximize revenues in the energy and reserve markets according to 2019 market prices. The model considers the day-ahead energy market and all the reserve products existing in France, distinguishing between reserve capacity and reserve energy products. By optimising the trade-offs between the day-ahead and the reserve markets, the storage hydropower plant increase its revenues. The pumped storage hydropower plant sometimes chooses the Frequency Containment Reserve market or the day-ahead market only. The apparition of some hours of FCR participation with the pumped storage plant is explained by its higher number of generating hours and by the higher volatility of reserve energy prices. These two factors also explain the higher efficiency of incentive measures with the pumped storage plant.