To meet the European Union's 2050 climate neutrality target, future electricity generation is expected to largely rely on variable renewable energy (VRE). VRE supply, being dependant on weather, is susceptible to changing climate conditions. Based on spatiotemporally explicit climate data under a Paris-proof climate scenario and a comprehensive energy conversion model, this study assesses the projected changes of European VRE supply from the perspective of average production, production variability, spatiotemporal complementarity, and risk of concurrent renewable energy droughts. For the period 2045–2055, we find a minor reduction in average wind and solar production for most of Europe compared to the period 1990–2010. At the country level, the impact of climate change on average VRE production is rather limited in magnitude (within ±3% for wind and ±2% for solar). The projected mid-term changes in other aspects of VRE supply are also relatively small. This suggests climate-related impacts on European VRE supply are less of a concern if the Paris-proof emission reduction pathway is strictly followed. Based on spectral analysis, we identify strong seasonal wind-solar complementarities (with an anticorrelation between -0.6 and -0.9) at the cross-regional level. This reduces the demand for seasonal storage but requires coordinated cross-border efforts to develop a pan-European transmission infrastructure. The risk of concurrent renewable energy droughts between a country and the rest of Europe remains non-negligible, even under the copperplate assumption. Central Western European countries and Poland are most vulnerable to such risk, suggesting the need for the planning of adequate flexibility resources.