It is possible to power up and down nuclear power plants, it is however very inefficient. And when you have neighbors wanting to buy your surplus electricity and a grid that support it, why bother?
France and other countries (like Switzerland) import electricity from time to time not because they are unable to produce it, but because it's cheaper to do so. Germany on the other hand have to import electricity when there not enough wind/sun and their coal plant are already maxed-out.
France in recent years relied on energy imports during winters, because they heat a lot with electricity[1], and e.g. in 2015 they had to temporarily shut down a lot of their nuclear plants due to "quality concerns"[2], tho that was not the first time other European nations had to save them from going dark.
Germany mostly has a positive import rate (importing more than exporting) during the summer mornings and evenings, mostly because it's less windy in summers, it's dark so no solar, foreign surplus energy is readily available and cheap so that it doesn't make sense to increase hard coal energy production for a few hours each.
But the coal plants are far from maxed out, and Germany does not rely on imports. E.g. during summer mornings when Germany imports about 4 GW to make up for lack of wind and solar, the hard coal plants produce 4-12 GW, meaning to avoid those imports you'd have to run them at 8-16 GW. Those plants alone can produce 19 GW easily, and that's just hard coal.
If you like playing with interactive charts about energy production in Germany and the import/export rate, Fraunhofer ISE offers https://www.energy-charts.de/
PS:
Since 2006 up until now, Germany had a negative annual import rate (more exports than imports)[3].
And the last month Germany imported (not necessarily had to import) more energy than exported was September 2011.
Coal plants in Germany have the same problem as elsewhere: They are becoming too expensive.
Renwable power in Germany is mostly a mix of solar and wind energy. In the summer, the curve of solar production fits nicely the daytime of the highest demand, while the higher production of wind energy is in cold stormy winter months. What needs to complement the mix are gas power plants which can be ramped up and down quickly. Coal plants are too slow for that.
France and other countries (like Switzerland) import electricity from time to time not because they are unable to produce it, but because it's cheaper to do so. Germany on the other hand have to import electricity when there not enough wind/sun and their coal plant are already maxed-out.