The Mont-Blanc massif, being iconic with its large glaciers and peaks of over 4,000 m, will experience a sharp increase in summer temperatures during the twenty-first century. By 2100, the impact of climate change on the cryosphere and hydrosphere in the Alps is expected to lead to a decrease in annual river discharge. In this work, we modelled the twenty-first century evolution of runoff in the Arve river, downstream of Mont-Blanc's French side. For the first time for this region, we have forced a hydrological model with output from an ice-dynamical glacier model and 16 downscaled climate projections, under RCP4.5 and RCP8.5 scenarios. By 2100, under RCP8.5 (high-emission scenario), the winter discharge of the Arve river remains low but is expected to increase by 80% when compared to the beginning of the century. By contrast, the summer season, currently the most important discharge period, will be marked by a runoff decrease of approximately 40%. These changes are almost similar according to a scenario with a lower warming (RCP4.5) and are mostly driven by glacier retreat. These shifts will have significant downstream impacts on water quantity and quality, affecting hydroelectric generation, agriculture, forestry, tourism and aquatic ecosystems.