In France last summer, some plants had indeed to be shut down because of the drought but:

* a minority of plants were involved, it was only an issue because it happened on top of other issues (planned maintenances delayed due to covid, corrosion issues)

* the problem isn't actually the drought, it was the heat. The plants could keep operating, but they would have rejected water too hot, in breach of environmental regulations.

Besides, new plants can be built close to the sea instead of rivers to account for that.