By 2050, the European Union aims to cut the European CO2 emissions by 80-95% compared to 1990. To reach this target, the European power grid plays a key role to ensure both a low-carbon and affordable electricity supply. In this context, the e-Highway2050 project identifies the European grid architectures, which would be needed under five contrasted low-carbon energy scenarios. An innovative approach based on Monte-Carlo simulations of the European power system, modeled with approximately one hundred zones, ensures both robustness of the results and the possibility to consider all of Europe at once. A detailed cost-benefit analysis of the different grid architectures shows their high profitability. Their implementation between 2030 and 2050 in terms of transmission requirements and technological solutions is discussed.