Invasive fishes are a major environmental issue at the global scale, particularly for their impacts on freshwater ecosystems via the mechanisms of hybridisation, competition, predation, and disease transmission. This is of special conservation concern on the Iberian Peninsula due to the high level of endemism. With the aim to improve our knowledge on the invasion process of non‐native fishes, the present study consists of analysing key biological traits potentially related to their colonisation capacity: morphology, parasite communities, and genetic diversity. A non‐native population of Languedoc minnow Phoxinus septimaniae (leuciscid species native to south‐east France) was assessed in Tordera Stream (north‐eastern Iberian Peninsula). Fish were sampled in mid‐May (reproductive period) 2018 and 2019. Biological traits were compared between colonising and resident individuals from stream reaches of intermittent and perennial flow, respectively. After adjusting for fish size/body mass with analysis of covariance, body condition and health status (external and internal examination) tended to be better in the intermittent reach. Parasite load (number) and diversity (Shannon index) were significantly higher in the perennial reach. Fish development was also more stable in colonising minnow, as detected by low levels of fluctuating asymmetry for the eye diameter and the length of pectoral fins (adjusted for bilateral character size). Genetic diversity (microsatellite markers) was lower in resident minnow. Minnow genetic homozygosity (index of internal relatedness) was positively associated with parasite load and developmental instability (high fluctuating asymmetry levels). Our results show that colonising minnows display particular profiles of morphological, parasitological, and genetic traits that apparently allow these individuals to increase their dispersal capacity to survive and reproduce in harsher environmental conditions. The potential mechanisms may be related to a wider physiological tolerance, better immune response, parasite resistance/tolerance, and genetic diversity in colonising specimens. Such information reveals the specific traits of successful fish invaders under a seasonal colonisation dynamic. These data are relevant for environmental managers, to predict and identify areas vulnerable to invasion, in order to establish monitoring programmes for early detection, which will help to reduce the spread of non‐native fish populations.