I believe the French facilities have the capacity of doing load following, but are not doing it because it is less efficient (and therefore more expensive). So I would also not say "days", but it is also true that one cannot directly take a situation where nuclear has, so far, being used only for base load and pretend that load following will work exactly the same way.

I'm not sure why you say "rare, extreme peaks": the current demand is non-flat every day, with a difference between the trough and peak that is typically ~50% of the peak.

I agree that large scale battery storage is challenging. Maybe the solution would be to have some storage and some "wasted efficiency" by using nuclear plants in load following and turning them in stand-by every day during off-peak hours.