It's true, nuclear energy costs more, but you're avoiding the elephant in the room and don't address the core issue that solar and wind energies are intermittent, and that you will anyways need to use some controllable energy source (batteries, coal plans, nuclear plans...) to offset this issue.
The part about public protests is kind of cliché, as a french myself, rising the electricity prices happened and people were fine. The protests happened mostly for the oil prices. One thing about french electricity, is that because of the European agreement "ARENH" [1] (will end in 2025), they are forced to sell at capped price to private actors, in order to boost the competition. If this wasn't the case, then maybe the nuclear power sector could be much less costly, or profitable.
[1]: https://www.conseil-etat.fr/en/news/rising-energy-prices-the...