In recent years, forests all around the world have experienced increased mortality induced by heat waves and extreme drought events related to climate change. Forecasting the long-term future of forest ecosystems and tree species under a changing environment necessarily raises the issue of evolutionary dynamics. Questions are being raised about the potential for long living organisms such as trees to adapt to a rapid climate change and the extent to which our management actions on forests affect the evolutionary responses of tree species. Additionally, in mixed forests, interspecific interactions can affect the probability of evolutionary rescue of species. As tackling these questions is difficult with experimental approaches, the impacts of climate change on forests are frequently investigated through modelling approaches. Yet, species evolution has often been missed from current models predicting the consequences of global warming on forests. In this study, we therefore propose an approach that integrates evolution into a multi-species, process-based forest model that has been validated on forest inventory data, to test eco-evolutionary hypotheses and explore potential impacts of forest management practices on the fate of forests. Here, we illustrate our approach with a case study in which we showed that greater trait variability and heritability reduced the lost of forest cover after drought induced mortality events, over a short timescale (century). We also showed that adding new species into the forest improved recovery after climate change but could also prevent the evolutionary rescue of local species.