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.
I'm sure, they can figure that out with something similar to irrigation channels and/or solar panels along river/channels to prevent evaporation. Would they do this? That's another question
Would that help though, if drought periods hit Western Europe, like last year, and water levels in the rivers are as low as they were?