Many studies have been carried out on predictive traits, such as geographical range, but most of them were related to introduced species and considered the invasion as a whole. The contrasting results previously obtained suggest that studies should take into account the dynamics of the invasion process (immigration, establishment, spread). We hypothesise that the geographical range reflects the species tolerance to new environments, and is related especially to the establishment and spread of the invasion process. First, data on spontaneous invasive birds in France since 1950 were collected to determine the relation between geographical range and spontaneous invasions of French biogeographical areas. Second, the urban context, assumed to be free of immigration, was used to focus on this relation during the establishment and spread of species. For all species recorded, we determined the geographical range from an atlas, measured as the distribution range area RA (occupied area in km2) and the latitudinal range LR (km from north to south). Our results on spontaneous invaders show that the geographical range, especially RA, could help to predict the extent of an invasion once it has started. In the urban context, RA and LR discriminated urban colonists from urban avoiders, which supported the link between the geographical range and establishment/spread success. The geographical range participates, with other traits, in defining an ‘ideal invader'. We suggest that the dynamics of the invasion process i.e., considering each step of invasion rather than an entity, should be an important conceptual tool for future predictive studies.