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I imagine the third option is that they could run the cooling water in a loop with some really big radiators and not take water from the river at all if they wanted, but it would be very expensive.
I don’t think you’d want to tie your ability to cool the reactor to outside air temperatures. Bodies of water do warm up, but are generally a much better “ultimate heat sink”.
Eh, as long as you designed it with a reasonable factor of safety (say, highest temperature ever recorded at that location +5C, maybe) it'd be fine. I think the cost is a far, far bigger issue because the radiator necessary would be absolutely gigantic. Plus if you've got fans cooling it (so you can make it smaller) instead of passively cooling it, that's another point of failure, although I suppose if getting river water relies on pumps then it isn't any worse.
Typical safety margins for weather use 50 or 100 year events. The system that is rated for that weather event has a margin in it. Roofs, for example, are designed to withstand the snow loads for the worst snow storm in 50 years but the truss systems which are rated to handle that load can handle more.
I know, but the safety margin for a nuclear reactor should be atypical.
Some places use the waste heat for district heating, in which case the waste heat isn't really a waste any more. I don't know if France does that, though. The Soviet Union was super-big on district heating. That won't consume all of the heat, and it really just gets you cheap heating for the city -- like, a large power plant will generate more heat than you actually need to heat a city.
In the US, we historically had some very limited district heating, though that was driven off waste heat from fossil fuel power plants, where you can do the same thing.
If you can make use of the heat output directly, it's an area where thermal options (fossil fuels, nuclear, geothermal, solar thermal) compare particularly favorably to non-thermal options (solar panels, wind, hydroelectric), because there the thermal options don't need to see the efficiency reduction from conversion to electricity and back.
googles
Sounds like they aren't currently using the heat for district heating (or at least some aren't), so they could probably use at least some of the heat some of the time for that.
https://www.sciencedirect.com/science/article/abs/pii/S0301421518300533
That being said, the time when anyone cares about water flows and river temperatures is presumably the summer, and that's also going to be when there's less demand for heat. So it's more a way to get heating more-efficiently than an alternative to dumping heat somewhere.
Unless you're gonna create some absolutely colossal thermal energy store that could span seasons, like, put a cover on a lake, heat it up in the summer, and then use that heat in the winter.
The other issue is that in order to provide district heating you've got to put your power plant next to a city instead of in the middle of nowhere, like we prefer to do in the US (especially for nuclear).
I think for the US, the structure of the city is also a factor.
This is painting with a broad brush, but:
American cities tend to have a very high-density core that has offices and stores and such, and are surrounded by a lot of low-density housing.
European cities tend to have a medium-density, about four stories, across the city.
That's a function of the fact that a lot of the US was constructed after the invention of the elevator (which allows for taller building heights to be practical; historically, top floors were undesirable) and the automobile (which allows for lower-density housing to be practical). There are few skyscrapers in Europe; Turkey actually has the most, by a huge margin, and like the US, Turkey saw a lot of population growth in the 20th century, so a lot of Turkey is gonna be new-build.
I spent a while looking at the few US district heating systems that existed in the past (and a few, now). They don't do the suburbs -- they provided heating to that high-density city core. There, they don't have to run pipes a long distance to transport heat; electricity is cheaper to transport than heat.
There are exceptions that do provide district heating to residences, like Manhattan, but Manhattan is also a (partial) exception to the "high-density core, low-density suburbs" structure; New York City, though the largest American city, doesn't look much like a typical American city:
https://en.wikipedia.org/wiki/New_York_City_steam_system
https://streeteasy.com/blog/steam-heat-in-new-york-city-explainer/
But for the general case, I expect that it's gonna make less economic sense to do district heating of housing in the US than in Europe.