The Paris Agreement promotes forest management as a pathway towards halting climate warming through the reduction of carbon dioxide (CO2) emissions1. However, the climate benefits from carbon sequestration through forest management may be reinforced, counteracted or even offset by concurrent management-induced changes in surface albedo, land-surface roughness, emissions of biogenic volatile organic compounds, transpiration and sensible heat flux2–4. Consequently, forest management could offset CO2 emissions without halting global temperature rise. It therefore remains to be confirmed whether commonly proposed sustainable European forest-management portfolios would comply with the Paris Agreement—that is, whether they can reduce the growth rate of atmospheric CO2, reduce the radiative imbalance at the top of the atmosphere, and neither increase the near-surface air temperature nor decrease precipitation by the end of the twenty-first century. Here we show that the portfolio made up of management systems that locally maximize the carbon sink through carbon sequestration, wood use and product and energy substitution reduces the growth rate of atmospheric CO2, but does not meet any of the other criteria. The portfolios that maximize the carbon sink or forest albedo pass only one—different in each case—criterion. Managing the European forests with the objective of reducing near-surface air temperature, on the other hand, will also reduce the atmospheric CO2 growth rate, thus meeting two of the four criteria. Trade-off are thus unavoidable when using European forests to meet climate objectives. Furthermore, our results demonstrate that if present-day forest cover is sustained, the additional climate benefits achieved through forest management would be modest and local, rather than global. On the basis of these findings, we argue that Europe should not rely on forest management to mitigate climate change. The modest climate effects from changes in forest management imply, however, that if adaptation to future climate were to require large-scale changes in species composition and silvicultural systems over Europe5,6, the forests could be adapted to climate change with neither positive nor negative climate effects.