France has a latitudinal range for the expansion of Aedes albopictus invasive populations that is not yet completely colonized providing a critical opportunity to address key invasion processes. We propose a spatio-temporal model (DISTIGRI) to describe and predict current and future expansions at intra- and inter-annual scales of A. albopictus. This process-based model integrates mechanistic descriptions of the developmental cycle and the dispersal process of A. albopictus within a reaction-diffusion framework, depending on climatic suitability and photoperiod with a high spatio-temporal resolution. Using this model coupled with a climatic database, we propose several maps describing the current intra-annual distribution of A. albopictus, including the date of first emergence and the length of the period with significant adult presence. We also compute its future distribution over the next 10 years under several climatic scenarios, which shows a range expansion with a strong dependence on the climatic scenario. The outputs of the model may constitute a valuable asset for designing control and avoidance strategies, and to anticipate the biting nuisance with a high spatio-temporal resolution. These outputs also emphasize the importance of taking dispersal and life cycle into account to obtain accurate descriptions of out-of-equilibrium processes such as ongoing invasions.