The worst problem is that the French nuclear reactors have massive issues - over half their capacity is currently offline because of massive defects or barely producing due to a lack of cooling water [1]. That same drought also impacted Swiss nuclear plants [2] and Italian hydro power [3].
On top of that, the German gas peaker plants that used to be relatively cheap are now, thanks to the Russian invasion, extremely expensive - but since the French don't have an alternative, they pay absurd amounts of essentially government-funded money [4] on the spot markets, enough to make even the expensive gas peakers worth it, which in turn drives up the price for anyone else on the shared European electricity grid.
And to make the situation even worse than it already is, this is not just a spot market crisis. There is no indication at all that the situation in France will clear up any time soon - to the contrary, it will get exponentially worse in winter, as the majority of France uses electric heating - and the drought induced hydro crunch will need many months of constant rainfall to refill all the natural reservoirs before the plants can act at capacity again. This makes long-term electricity futures absurdly expensive as well, and the price hike of these futures hasn't even begun to reach electricity consumers yet.
[1] https://news.ycombinator.com/item?id=32605337
[2] https://www.swr.de/swraktuell/baden-wuerttemberg/suedbaden/a...
[3] https://www.politico.eu/article/europe-scorching-summer-heat...
[4] https://www.lemonde.fr/en/energies/article/2022/07/28/energy...