Not building new nuclear power plants in the last 30 years was a major mistake, in terms of energy supply security as well as CO2 emissions.
French generation is ~70% nuclear (10% wind/solar) and German is ~10% (~40% wind/solar). Yet their prices track each other closely. So I think this explanation is too simplistic. Possibly there are large interconnects between the French and German grids levelling out wholesale prices, but my assumption is that they cannot carry enough power for this imagined scenario where nuclear makes a big difference.
Now, if you produce electricity by burning gas that you import and gas prices go through the roof then your production costs follow and your stuck.
In the meantime, production costs of nuclear plants have not moved at all. Which makes controlling consumer prices much more doable and less costly, for instance, you can sell that electricity with improved profit margins (and France does export a lot of electricity).