As wind and solar power provide a growing share of Europe's electricity, understanding and accommodating their variability on multiple timescales remains a critical problem. On weekly timescales, variability is related to long-lasting weather conditions, called weather regimes, which can cause lulls with a loss of wind power across neighbouring countries. Here we show that weather regimes provide a meteorological explanation for multi-day fluctuations in Europe's wind power and can help guide new deployment pathways that minimize this variability. Mean generation during different regimes currently ranges from 22 GW to 44 GW and is expected to triple by 2030 with current planning strategies. However, balancing future wind capacity across regions with contrasting inter-regime behaviour-specifically deploying in the Balkans instead of the North Sea-would almost eliminate these output variations, maintain mean generation, and increase fleet-wide minimum output. Solar photovoltaics could balance low-wind regimes locally, but only by expanding current capacity tenfold. New deployment strategies based on an understanding of continent-scale wind patterns and pan-European collaboration could enable a high share of wind energy whilst minimizing the negative impacts of output variability.