Oak (Quercus petraea (Matt.) Liebl. and Quercus robur L. grouped), European beech (Fagus sylvatica L.) and hornbeam (Carpinus betulus L.) are three major species of western and central European forests. When conditions are suitable for the three species, silvicultural management often favours oak because of its greater economic interest. Forest managers know that beech and hornbeam are strong competitors for oak during the regeneration phase, but the conditions that influence the relative success of the regeneration of the three species growing in mixture are still poorly characterised. The natural regeneration of the three species 20 years after canopy openings was studied based on 108 study sites established in 2001 in French forests impacted by the windstorms Lothar and Martin in 1999. In spring and summer 2018 and 2019, all saplings over 0.1 m in height were counted, species were identified and diameter at breast height (DBH) was measured for all saplings over 1.30 m. The height of the saplings with the highest and median DBH in each plot was recorded for each species. Mixed models were used to analyse the combined effects of former stand type, distance from the edge of the gap and soil conditions on species presence, sapling abundance, DBH and height. The modelling approach highlighted the preponderant role of the initial seed rain on the presence and sapling density of the three species compared to interspecific competition or distance from the edge. The two latter factors had a secondary effect on sapling DBH and height. Beech and hornbeam saplings were more abundant than oak saplings regardless of soil conditions (on average, 3097, 3063 and 344 saplings ha−1, respectively), suggesting a strong competitive ability of these two species. Oak was present on 22% (43% for hornbeam and 68% for beech) of the studied plots, at a low density but with a height and DBH similar to that of beech or hornbeam. This result highlights the high dissemination capacity of beech and hornbeam, which prevents the establishment of a stand dominated by oak. When seeking to obtain oak-dominated stands in the lowlands of Europe, the abundance of beech and hornbeam can be a limiting factor that could lead to the disappearance of oak from large areas if no silvicultural operations are performed to promote it.