So, yes, indeed, Google can stop providing search for the whole France.
It should be able to just de-list news sources for French searchers. Again, I can’t see this surviving a non-French EU court. If it did, zeroing resources to crawling French news sites would be a reasonable response.
All that said, this is a silly way to go about subsidising local news. If France wants its newspapers, subsidise them. Don’t force an American company to provide you with a service and then make them pay for it.
It's already done, let's note.
Except it's not. I never use Google, I use DuckDuckGo. If DDG fails I try Bing. I have google and facebook domains blocked from access in my system because I don't like their tracking. Lots of other people search without Google. Google is simply not a monopoly in the search game.
And the fact that you can use another search engine doesn't change the power Google has, because everyone else uses Google. So your website has to play by Google's rules if you want to be found.
The fact is, despite some politicians declaring it a fundamental right, the news does not provide enough value to most people for them to pay for it.
There is an absolute glut of content out there, way way more than anybody wants or needs. Much of it is less than worthless, it's actually of negative value because it's designed to hijack your attention. Remove the infusion of ad money that is producing this, let it settle to the things that people are actually willing to pay for, and we'll all be better off.
If i pay for a news site, i would go directly to it, and i would not care about hundreds of other paywalled results that i would not pay for.