Electric carsharing systems allow individuals to borrow electric cars on a short-term basis for a rental rate charged by the time or the distance driven. These systems are seen as a promising way to both lower the CO2 emissions linked to urban mobility and reduce urban congestion through a decrease in the number of privately owned cars parked in cities. We focus on the optimal long-term design of a station-based carsharing system in which shared cars should be picked-up and dropped off by customers at stations. More precisely, we seek to determine the number of chargers to build in each station and the size of the vehicle fleet to deploy in the network. One major difficulty here is that to be practically relevant, the modelling of this strategic problem should be able to estimate the future revenue that one may get by operating the proposed system on a daily basis. Our model should thus consider operational decisions such as trip request acceptance, car dispatching to stations, intra-day car charging and relocation. Furthermore, in practice, uncertainties on the trip duration and energy consumption may prevent cars from being available when and where needed with a sufficient battery state of charge. To handle this difficulty, we first propose a new scenario-based two-stage stochastic programming approach. We then seek to assess the value of a stochastic solution by discussing numerical results carried out on randomly generated instances.