Shared autonomous vehicles (SAVs) are the next major evolution in urban mobility. This technology has attracted much interest of car manufacturers aiming at playing a role as transportation network companies (TNCs) in order to gain benefits per kilometer and per ride. The majority of future SAVs will most probably be electric. It is therefore important to understand how limited vehicle range and the configuration of charging infrastructure will affect the performance of shared autonomous electric vehicle (SAEV) services. We aim to explore the impacts of charging station placement, charging type (rapid charging, battery swapping) as well as vehicle range onto service efficiency and customer experience in terms of service availability and response time. We perform an agent-based simulation of SAEVs across the Rouen Normandie metropolitan area in France. The simulation process features impact assessment by considering dynamic demand responsive to the network and traffic. Research results suggest that the performance of SAEVs is strongly correlated to the charging infrastructure. Importantly, faster charging infrastructure and optimized placement of charging locations in order to minimize distances between demand hubs and charging stations result in a higher performance. Further analysis indicates the importance of dispersing charging stations across the service area and how this affects service effectiveness. The results also underline that SAEV battery capacity has to be carefully selected to avoid the overlaps between demand and charging peak times. Finally, the simulation results show that by providing battery swapping infrastructure the performance indicators of SAEV service are significantly improved.