*Background. Like conventional crops, some GM cultivars may readily hybridize with their wild or weedy relatives. The progressive introgression of transgenes into wild or weedy populations thus appears inevitable, and we are now faced with the challenge of determining the possible evolutionary effects of these transgenes. The aim of this study was to gain insight into the impact of interspecific hybridization between transgenic plants and weedy relatives on the evolution of the weedy phenotype. *Methodology/Principal Findings. Experimental populations of weedy birdseed rape (Brassica rapa) and transgenic rapeseed (B. napus) were grown under glasshouse conditions. Hybridization opportunities with transgenic plants and phenotypic traits (including phenological, morphological and reproductive traits) were measured for each weedy individual. We show that weedy individuals that flowered later and for longer periods were more likely to receive transgenic pollen from crops and weed×crop hybrids. Because stem diameter is correlated with flowering time, plants with wider stems were also more likely to be pollinated by transgenic plants. We also show that the weedy plants with the highest probability of hybridization had the lowest fecundity. *Conclusion/Significance. Our results suggest that weeds flowering late and for long periods are less fit because they have a higher probability of hybridizing with crops or weed×crop hybrids. This may result in counter-selection against this subset of weed phenotypes, and a shorter earlier flowering period. It is noteworthy that this potential evolution in flowering time does not depend on the presence of the transgene in the crop. Evolution in flowering time may even be counter-balanced by positive selection acting on the transgene if the latter was positively associated with maternal genes promoting late flowering and long flowering periods. Unfortunately, we could not verify this association in the present experiment.