The assessment of climate change impacts on biodiversity has so far been biased toward the taxonomic identification of the species likely either to benefit from climate modifications or to experience overall declines. There have still been few studies intended to correlate the characteristics of species to their sensitivity to climate change, even though it is now recognized that functional trait-based approaches are promising tools for addressing challenges related to global changes. In this study, two functional indices (originality and uniqueness) were first measured for 35 fish species occurring in French streams. They were then combined to projections of range shifts in response to climate change derived from species distribution models. We set out to investigate: (1) the relationship between the degrees of originality and uniqueness of fish species, and their projected response to future climate change; and (2) the consequences of individual responses of species for the functional diversity of fish assemblages. After accounting for phylogenetic relatedness among species, we have demonstrated that the two indices used measure two complementary facets of the position of fish species in a functional space. We have also rejected the hypothesis that the most original and/or less redundant species would necessarily experience the greatest declines in habitat suitability as a result of climate change. However, individual species range shifts could lead simultaneously both to a severe decline in the functional diversity of fish assemblages, and to an increase in the functional similarity among assemblages, supporting the hypothesis that disturbance favors communities with combination of common traits and biotic homogenization as well. Our findings therefore emphasize the importance of going beyond the simple taxonomic description of diversity to provide a better assessment of the likely future effects of environmental changes on biodiversity, thus helping to design more effective conservation and management measures.