High genetic variation and extensive gene flow may help forest trees with adapting to ongoing climate change, yet the genetic bases underlying their adaptive potential remain largely unknown. We investigated range-wide patterns of potentially adaptive genetic variation in 64 populations of European beech (Fagus sylvatica L.) using 270 SNPs from 139 candidate genes involved either in phenology or in stress responses. We inferred neutral genetic structure and processes (drift and gene flow) and performed differentiation outlier analyses and gene-environment association (GEA) analyses to detect signatures of divergent selection. Beech range-wide genetic structure was consistent with the species' previously identified postglacial expansion scenario and recolonization routes. Populations showed high diversity and low differentiation along the major expansion routes. A total of 52 loci were found to be putatively under selection and 15 of them turned up in multiple GEA analyses. Temperature and precipitation related variables were equally represented in significant genotype-climate associations. Signatures of divergent selection were detected in the same proportion for stress response and phenology-related genes. The range-wide adaptive genetic structure of beech appears highly integrated, suggesting a balanced contribution of phenology and stress-related genes to local adaptation, and of temperature and precipitation regimes to genetic clines. Our results imply a best-case scenario for the maintenance of high genetic diversity during range shifts in beech (and putatively other forest trees) with a combination of gene flow maintaining within-population neutral diversity and selection maintaining between-population adaptive differentiation.