Residential prosumers with photovoltaic and battery storage systems (BSS) can optimize the return on their investment in two main ways, increasing self-consumption and providing demand response (DR) to various electricity markets. In this paper, we investigate the potential benefits for French prosumers from providing DR to the capacity market and to a specific DR market, the Notifications d'Echange de Blocs d'Effacement (Demand Response Block Exchange Notifications-NEBEF). An optimization model is developed which would allow the prosumer to bid in the two markets. We consider the uncertainty affecting consumption and three retail rates. We also assess the impact of a compensation scheme for a balance-responsible party when DR is activated inside their balancing area. We show that DR volumes can represent about 20% of self-consumption but this falls to 6% due to uncertainty and payments compensating the supplier. Overall savings from self-consumption and the yield from DR are too low in France to cover the cost of investing in a BSS. A DR premium from 18.7 to 62 ctseuro/kWh is needed to reach the BSS break-even point. These numbers drop when considering time-of-use tariffs compared to a flat retail rate.