Yes, Europeans are aiming at a trans-national structure - that is part and parcel of what the EU is about - but it doesn't involve all of the tinfoil conspiracy crap that comes along with the word "globalism ". One might as well be speaking of some latter-day alternative to the Protocols of the Elders of Zion.
You're hung up on the emotions around the word globalism. Thats by design, to marginalize anyone who would resist what they are doing.
The EU addresses Europe, which is why there has been so much pressure against the UK for Brexit. They cannot allow any dissent.
Its also behind the free trade laws here in North America. Its why they wont enforce the border. Massive immigration has turned much of the South West United States into Mexico. Things like building the super highway they want, allowing Mexican trucks, and encouraging illegal immigration are all designed to dilute our national identity.
The end state is removal of our Constitutionally protected rights and subordination to Brussels.