Nuclear is the worst possible option to fill said gaps. Nuclear reactor need to run at a mostly stable output permanently, they are slow to react to changes and can’t be switched on or off at will.
You could use them to generate a stable base power level, but that’s the opposite of what we need. It wouldn’t change anything regarding the need of energy storage.
The best option currently as a gap filler is gas cause it can be turned on or off in minutes when needed.
Not keeping up with demand is a self-made problem. Multiple EU countries already have multiple days a year where they use 100% renewables.