Remote island communities face problems caused by the continuity and reliability of their power supply, which tend to be exacerbated when they rely on fluctuating renewables. In this paper the sizing of supply-demand-storage schemes is addressed in respect of their economy and feasibility. In the case of the French Atlantic Island of Yeu, high electricity peaks are common, due to tourism and to the seasonal use of second homes. A power plant dispatching model is used to simulate energy scenarios in 2030, subject to the supply-demand power equilibrium and the requirements of hydrogen-powered boats. Interconnected Yeu Island could accommodate 30 MW of renewables without curtailment, ensuring an electricity independence rate of 86% and renewable energy generation rate of 131% in the load, made up of wind (42%), solar (10%), tidal (21%), wave energy (25%) and biomass (2%). Excess energy could be exported through bidirectional cables, which are also the key adjustment variable in the reserve margins. Energy transition costs amount to 112 M€ in renewable-hydrogen projects, and 3 M€ for demand-side measures achieving a 2.7% reduction in load. An island self-sufficient power system with Yeu load characteristics would require at least 40 MW of variable renewables and 1 GWh energy storage capacity, at costs of 1.15 Bln€.