This study aimed to simulate oak and beech forest growth under various scenarios of climate change and to evaluate how the forest response depends on site properties and particularly on stand characteristics using the individual process-based model HETEROFOR. First, this model was evaluated on a wide range of site conditions. We used data from 36 long-term forest monitoring plots to initialize, calibrate, and evaluate HETEROFOR. This evaluation showed that HETEROFOR predicts individual tree radial growth and height increment reasonably well under different growing conditions when evaluated on independent sites. In our simulations under constant CO2 concentration ([CO2]cst) for the 2071-2100 period, climate change induced a moderate net primary production (NPP) gain in continental and mountainous zones and no change in the oceanic zone. The NPP changes were negatively affected by air temperature during the vegetation period and by the annual rainfall decrease. To a lower extent, they were influenced by soil extractable water reserve and stand characteristics. These NPP changes were positively affected by longer vegetation periods and negatively by drought for beech and larger autotrophic respiration costs for oak. For both species, the NPP gain was much larger with rising CO2 concentration ([CO2]var) mainly due to the CO2 fertilisation effect. Even if the species composition and structure had a limited influence on the forest response to climate change, they explained a large part of the NPP variability (44% and 34% for [CO2]cst and [CO2]var, respectively) compared to the climate change scenario (5% and 29%) and the inter-annual climate variability (20% and 16%). This gives the forester the possibility to act on the productivity of broadleaved forests and prepare them for possible adverse effects of climate change by reinforcing their resilience.