The internet was designed to be resilient in the face of nuclear war. If it can't handle governments that actually protect their citizens from predation by multinational corporations, then we should rethink some things about the direction that we've taken with it.
I don't think that's what's happening here. This is about a French company being disallowed by France from selling French citizens' data to a US Company.
Maybe this decision makes France toxic/favorable to certain kinds of business--much like how many privacy companies operate in Switzerland because the Swiss government is less likely to snoop than certain others, or how advertising companies operate in the US because they'll let you do whatever you want to their citizens. So yeah, fragments.
But you as a user are free to opt-into any fragment of the internet that will have you. If your government wants to stop you from doing so you should either take it up with your government or circumvent those limitations.
I don't particularly like the kind of fragment that France is creating here, the notion that data has a physical location in space strikes me as a rather shaky one, and I think policies following therefrom are likely to create convoluted architecture that exfiltrates the benefits of access without exfiltrating database instances (I've written enough code that tap-dances around the GPDR to know). Since I'm not trying to start an ad supported business in France, though, I'm happy to respect their right to come up with whatever weird policies they want.
Would it be impossible? No. But would it be, say, 5x the amount of effort to build and maintain a federated system with no data stored across boundaries? Probably.