Questions have been raised about the ability of long-lived organisms, such as trees, to adapt to rapid climate change, and to what extent forest management actions influence the evolutionary responses of tree species. Given the life history of trees and the time scales involved, these questions are often addressed through modeling approaches. Yet, most of these works focus on single-species case studies. The main objective and originality of our work is to explore the evolutionary responses of tree species to climate change using a process-based model, in a multi-species context. This approach allows us to investigate the conditions necessary for evolutionary rescue in a mixed beech-fir forest. Additionally, we explored how adaptation measures, such as assisted gene flow and assisted migration affect the conditions for evolutionary rescue in this forest. To achieve these objectives, we integrated a quantitative genetic module into a process-based forest gap model, enabling species-specific parameters to evolve as quantitative traits under selective pressure and drift. Our results show that increased trait variability and heritability reduce the loss of forest cover following climatic warming in the short term (over a century). We also found that assisted gene flow had the expected effect of aiding species in tracking climate change. Finally, our study suggested that introducing new pre-adapted species into the forest could improve recovery after climate change but could also hinder the evolutionary rescue of local species. We conclude that integrating evolutionary dynamics into process-based models significantly enhances their predictive power by incorporating genetic adaptation scenarios that would otherwise be overlooked. This approach also allows to test eco-evolutionary hypotheses and better understand the potential consequences of adaptation measures to climate change for tree species.