Nit: If you're filing a flight plan, you do it with the country you're departing from. Even if you're piloting an aircraft departing into the US, it wouldn't have any effect on operations if you couldn't reach US websites. There's also several alternative ways for pilots to file flight plans outside of the web.

(The flight plans get passed between countries via AFTN/AMHS, which are dedicated telecommunications networks independent of the Internet.)

Europeans don't generally use .gov so if the US tries to pull that, they'll just block whatever .gov their VPN is hosted on.

Southern European countries are blocking whole Cloudflare IP ranges because of the massive grip on the government the sports licensing maffia has there. These countries also don't feature any direct flights to America as far as I can tell.

These blocks may cause (temporary) issues for American business relations and tourism, but such side effects may not be considered so problematic if the US leverages their government infrastructure to attack European legislators.

As a Brit/European, would I notice or care if fbi.gov was blocked via consumer internet providers? I'd probably not notice if *.gov was blocked. I'm fairly sure government-level internet provisioning has a very different set of restrictions to the general population for those who need access to US Gov services, in the same way that I'm sure the Chinese state itself isn't subject to the rules of the Great Firewall.

If a Govt decides that I am pretty sure they won't stop at anything but TLD level banning. Besides I don't know about other countries (or EU) but I won't be surprised if our giant industrious neighbour already has infrastructure in place just for such Trumpian shenanigans :)