Nuclear power is one of the most flexible sources of power, especially PWR's with ALFC or even more so - BWR's You can actually see how France is flexing in the summer on RTE website

The storage problem is home-made, because our problem is intermittent renewables that can't produce on-demand.

With consistent producers like nuclear there is no storage problem.

And of course the Natrium plant has the buffer so it can ramp grid output up and down while maintaining the reactor at consistent power levels.

France seems to work. They have plenty of nuclear power that is flexible. And you can have other forms of consumption flexibility; otherwise wind and solar are really in trouble.