There's no "massive defects" involved, it's a combination of 1. regular refueling maintenance which happens every summer; 2. some maintenance being delayed due to COVID-19 that was finally able to be scheduled this year; 3. a minor corrosion issue [1] being found with the welds in one of the newer plants, leading the power plant operator to stop all similar plants for safety reasons to be manually inspected.
> barely producing due to a lack of cooling water
There's plenty of cooling water, it's just warmer than usual upstream of some of the plants, and the plants have rules about not rejecting water above a certain temperature to the river in order to protect wildlife. These rules can be waived and in fact have been waived several times this summer and previous summers to continue producing at higher load -- it sucks for the fishes that get +1°C, but we're basically making a choice between warming up the rivers or warming up the planet with more CO2 emissions. This is indeed the same situation as in Beznau (CH, the article you linked), but absolutely not comparable to the problems with hydro in Italy that are actually due to lack of water. You can't waive a lack of water.
> no indication at all that the situation in France will clear up any time soon
(1) and (2) are absolutely going to clear up by winter. https://nuclear-monitor.fr/ shows the planned maintenance end dates. Just by the end of the month EDF is planning to have 11-12GW back online [2] (though their maintenance end dates tend to slip up by a few days in general). That leaves the 12 reactors (out of 56) impacted by (3). I suspect that if it actually comes to blackouts, (3) might also clear out, if we decide that the minor safety risk of the welding issues is less bad than the people actually dying due to lack of power. Unfortunately anything involving nuclear safety makes people freak out and require 100% reliability, even when it's absolutely irrational to do so and causes more human deaths.
[1] https://www.irsn.fr/FR/Actualites_presse/Actualites/Pages/20... [2] https://pbs.twimg.com/media/FbeQue0XkAAraJu?format=png&name=...