There's no technical reason why the reactors in question could not have kept running:
> "Due to the weather conditions and to comply with regulations on [cooling water] discharges, and thus to protect the environment," reactors at the Golfech, Bugey and Chooz plants, located on the banks of the Garonne, Rhône and Meuse rivers respectively, have been shut down, the EDF energy group told Agence France-Presse.
> The measure is an environmental protection requirement to avoid discharging too much hot water into rivers already warming from the heatwave. Power plants critical to the country's electricity production use river water to cool their reactors, which heats the water that is then released back into the river.
> The Economy Ministry on Saturday issued an exemption to the temperature limits for the heating of the Rhône around the Bugey plant "to ensure the security of the power grid," valid until July 20.
Similarly, all industrial processes of heat rejection, including data centers, could use closed cycle cooling, but they don't, because it's more expensive to install and operate.
That affects ~0.5% of the yearly production in France, it's not a "primary weakness", it's the opposite, it's so low of a problem that the state simply doesn't care enough to fix it.
And since the poster didn't knew that, I'm not sure the cost analysis holds up.
Well it's good that Germans chose coal over nuclear!