Invasion of new territories by insect vector species that can transmit pathogens is one of the most important threats for human health. The spread of the mosquito Aedes albopictus in Europe is emblematic, because of its major role in the emergence and transmission of arboviruses such as dengue or chikungunya. Here, we modeled the spread of this mosquito species in France through a statistical framework taking advantage of a long-term surveillance dataset going back to the first observation of Ae. albopictus in the Metropolitan area. After validating the model, we show that human activities are especially important for mosquito dispersion while land use is a major factor for mosquito establishment. More importantly, we show that Ae. albopictus invasion is accelerating through time in this area, resulting in a geographic range extending further and further year after year. We also show that sporadic "jump" of Ae. albopictus in a new location far from the colonized area did not succeed in starting a new invasion front so far. Finally, we discuss on a potential adaptation to cooler climate and the risk of invasion into Northern latitudes.