Solar doesn't work at night of course, but wind power does. Actually, on average, it is stronger at night. Yes, we have to supply power in the times of low renewable production. Though there are renewables which are good for it like biomass and water. Nuclear is the worst to accompany renewables, because it is the slowest power source from a load switching perspective. Gas is the one which is fast switching, that is why the typical peaker plants run on gas. They could run on oil of course, but that would be much worse. In the future, the gas is to be produced renewable, and of course energy storate has to be extended.

It’s not about “producing renewable”, it is about CO2 emissions (and about not empowering certain gas-exporting countries).

Right, but the renewables are the one power source which is well suited going into the future. They don't use up any non-renewable source (hence the name), and they are the one energy production which is really available in most countries. All the others more or less depend on imports.

Nuclear can not follow load fluctuations, so nuclear needs gas (or hydro).

And before the inevitable comment follows, yes, that may change with future technology. Just like everything else.

It can follow the fluctuations during the day. That's what is done in France. It is not efficient at all since a NPP cost mostly the same regardless of its power generation, and is technically a bit more complex, but perfectly doable.