Since its emergence in Yap Island in 2007, Zika virus (ZIKV) has affected all continents except Europe. Despite the hundreds of cases imported to European countries from ZIKV-infested regions, no local cases have been reported in localities where the ZIKV-competent mosquito Aedes albopictus is well established. Here we analysed the vector competence of European Aedes (aegypti and albopictus) mosquitoes to different genotypes of ZIKV. We demonstrate that Ae. albopictus from France was less susceptible to the Asian ZIKV than to the African ZIKV. Critically we show that effective crossing of anatomical barriers (midgut and salivary glands) after an infectious blood meal depends on a viral load threshold to trigger: (i) viral dissemination from the midgut to infect mosquito internal organs and (ii) viral transmission from the saliva to infect a vertebrate host. A viral load in body ≥4800 viral copies triggered dissemination and ≥12,000 viral copies set out transmission. Only 27.3% and 18.2% of Ae. albopictus Montpellier mosquitoes meet respectively these two criteria. Collectively, these compelling results stress the poor ability of Ae. albopictus to sustain a local transmission of ZIKV in Europe and provide a promising tool to evaluate the risk of ZIKV transmission in future outbreaks.