Background: Since its emergence in 2007 in Micronesia and Polynesia, the arthropod-borne flavivirus Zika virus (ZIKV) has spread in the Americas and the Caribbean, following first detection in Brazil in May 2015. The risk of ZIKV emergence in Europe increases as imported cases are repeatedly reported. Together with chikungunya virus (CHIKV) and dengue virus (DENV), ZIKV is transmitted by Aedes mosquitoes. Any countries where these mosquitoes are present could be potential sites for future ZIKV outbreak. We assessed the vector competence of European Aedes mosquitoes (Aedes aegypti and Aedes albopictus) for the currently circulating Asian genotype of ZIKV. Methodology/Principal Findings: Two populations of Ae. aegypti from the island of Madeira (Funchal and Paul do Mar) and two populations of Ae. albopictus from France (Nice and Bar-sur-Loup) were challenged with an Asian genotype of ZIKV isolated from a patient in April 2014 in New Caledonia. Fully engorged mosquitoes were then maintained in insectary conditions (28°±1°C, 16h:8h light:dark cycle and 80% humidity). 16–24 mosquitoes from each population were examined at 3, 6, 9 and 14 days post-infection to estimate the infection rate, disseminated infection rate and transmission efficiency. Based on these experimental infections, we demonstrated that Ae. albopictus from France were not very susceptible to ZIKV. Conclusions/Significance: In combination with the restricted distribution of European Ae. albopictus, our results on vector competence corroborate the low risk for ZIKV to expand into most parts of Europe with the possible exception of the warmest regions bordering the Mediterranean coastline.