Originating from African forests, Zika virus (ZIKV) has now emerged worldwide in urbanized areas, mainly transmitted by Aedes aegypti mosquitoes. Although Aedes albopictus can transmit ZIKV experimentally and was suspected to be a ZIKV vector in Central Africa, the potential of this species to sustain virus transmission was yet to be uncovered until the end of 2019, when several autochthonous transmissions of the virus vectored by Ae. albopictus occurred in France. Aside from these few locally acquired ZIKV infections, most territories colonized by Ae. albopictus have been spared so far. The risk level of ZIKV emergence in these areas remains however an open question. To assess Ae. albopictus' vector potential for ZIKV and identify key virus outbreak predictors, we built a complete framework using the complementary combination of (i) dose-dependent experimental Ae. albopictus exposure to ZIKV followed by time-dependent assessment of infection and systemic infection rates, (ii) modeling of intra-human ZIKV viremia dynamics, and (iii) in silico epidemiological simulations using an Agent-Based Model. The highest risk of transmission occurred during the pre-symptomatic stage of the disease, at the peak of viremia. At this dose, mosquito infection probability was estimated to be 20%, and 21 days were required to reach the median systemic infection rates. Mosquito population origin, either temperate or tropical, had no impact on infection rates or intra-host virus dynamic. Despite these unfavorable characteristics for transmission, Ae. albopictus was still able to trigger and yield large outbreaks in a simulated environment in the presence of sufficiently high mosquito biting rates. Our results reveal a low but existing epidemic potential of Ae. albopictus for ZIKV, that might explain the absence of large scale ZIKV epidemics so far in territories occupied only by Ae. albopictus. They nevertheless support active surveillance and eradication programs in these territories to maintain the risk of emergence to a low level.