Neither can nuclear power. Nuclear power has significant and often unpredictable down-times making the power source not as reliable as one might think. In Sweden the availability for nuclear power is on average something like 85%. Availability depends on the age of the nuclear power plant, what the staff situation is and how tight the regulations are. Can't run the plant if most of the staff is home sick and tighter regulations means more downtime for inspections.
The availability for wind power in the North Sea is about 50%. Admittedly, lower than 85% but you can make up for it by building many wind farms.
> Currently, we’re paying 31 Euro cents in Germany per kWh while French customers whose grid has a large share of nuclear pay just 17 Euro cents per kWh on average.
That is an argument for tighter integration of electricity grids between countries. But also 31 - 17 = 14 cents/kWh. The cost of electricity isn't a problem for most households (in my household the static fee is the biggest expense even during the winter months).