Stream fish are expected to be significantly influenced by climate change, as they are ectothermic animals whose dispersal is limited within hydrographic networks. Nonetheless, they are also controlled by other physical factors that may prevent them moving to new thermally suitable sites. Using presence–absence records in 655 sites widespread throughout nine French river units, we predicted the potential future distribution of 30 common stream fish species facing temperature warming and change in precipitation regime. We also assessed the potential impacts on fish assemblages' structure and diversity. Only cold-water species, whose diversity is very low in French streams, were predicted to experience a strong reduction in the number of suitable sites. In contrast, most cool-water and warm-water fish species were projected to colonize many newly suitable sites. Considering that cold headwater streams are the most numerous on the Earth's surface, our results suggested that headwater species would undergo a deleterious effect of climate change, whereas downstream species would expand their range by migrating to sites located in intermediate streams or upstream. As a result, local species richness was forecasted to increase greatly and high turnover rates indicated future fundamental changes in assemblages' structure. Changes in assemblage composition were also positively related to the intensity of warming. Overall, these results (1) stressed the importance of accounting for both climatic and topographic factors when assessing the future distribution of riverine fish species and (2) may be viewed as a first estimation of climate change impacts on European freshwater fish assemblages.