Not sure which "younger generation" you've been speaking to as that's not been my experience working with them.
Most have no connection to being "anything", not in that sense, not British, not European, nothing. "National" or political identities like "European" don't appeal to them, because as you said, they are more globalist. They don't care about being seen as "European" anymore than they would as any other region on the planet. Your FBPE crowd might, but they are few and far between and don't represent the majority. Seriously, the "younger generation" don't give a shit as much as the +25 year old Millennials do.
If the world is truly becoming global, why all the focus on being "European"? Your argument makes no sense.