Yes, you have to comply with laws in all the countries where they operate.

If Facebook were to pull out from France, there is almost nothing that France could do to force Facebook to comply.

This is why Google left the Chinese market. They did not want (or, more specifically, their employees refused) to comply with certain Chinese laws.

By "pull out" do you mean Facebook would have to stop doing business with advertisers in France? As long as the servers are in another country, the French government would have to create a Great Firewall to stop its citizens from accessing that content.

"As long as the servers are in another country, the French government would have to create a Great Firewall to stop its citizens from accessing that content." Not really.

How to avoid Great Firewall, while blocking FB:

France could expect Facebook to deny requests for content originating in France, regardless of where FB servers are. No need for a Great Firewall; make FB implement the firewall.

Legal justification (if not ethical):

The server locations are irrelevant because the data has cross the border into France.

Enforcement (how to force FB to block itself):

Easy: make the executives criminally liable. Also, anyone working on FB infrastructure could be held criminally liable.

France is a big and important country, they have heft to get their way from companies like FB.

Geoblocking is common and if they are doing business in a country it's perfectly reasonable to expect them to do it as well as for the state taking measures to enforce non-compliance (though criminal liability of corporate executives is something we won't see anytime soon I guess).

What's not reasonable is to force them to block people in other countries (and also those taking significant efforts to conceal their identity) - at least there is no international law (compared to international deals) justifying that anyhow.

Yes, it means that facebook can't operate a company in france selling services in france and expect to ignore french law.

But then this is exactly down the road to authoritarianism.

I understand and support that companies have to comply to the laws of the country where they are operating/targeting an audience. If worldwide dispersion of content banned in your country is such a concern, you can either push it to the UN OR you make according deals with the states harboring the companies.

Otherwise you can go down the great firewall route and there's little difference between that and forcing hoster to effectively implement the firewall worldwide.

Real-life example: weed is legal in the Netherlands. So all neighbors could now force the Dutch to close all coffeeshops OR block all their citizens from entering the Netherlands. I don't see any difference to this case.

It's not about a law being internationally valid.

It's about courts in the EU imposing things on EU hosts. Facebook has legal subsidiaries in the EU.

Companies that are present in several countries do have to employ lawyers to comply with each country's law.

It's like when the SEC fines an EU bank. It's not that the SEC has jurisdiction in the EU, it's that the EU bank has a subsidiary in the US and does business there.

I repeatedly asserted I have no problem with hosts having having to comply to national/EU/trade-deal law.

But in my opinion compliance is reached if they just do geoblocking in the areas affected by the law/delete content if it's originating there? If someone uses a VPN he's basically traveling to another jurisdiction for all practical purposes?

Compliance is reached once you have complied with what the court has ordered :)

And you don't care if the court has the standards of an autocracy?

International validity of laws is a complicated, but two cases come to mind (both American Laws): FATCA and FCPA