I can't speak for the EU, but can compare a bit to the USA. We don't just identify ourselves as Americans, we also identify ourselves by our location in the USA, our party identity, religion or lack thereof, etc. so it isn't a nationalism thing for us so much. Most of us really don't spend a lot of time thinking of what we are, or are not, compared to the rest of the world. We just feel that we are already living in a good place and that is it...
The old version of Europe was a hotbed for the generation of wars.
A unified, in purpose, Europe should minimize that. Having a common monetary system and legal system has to be a good thing.
A common language would probably be too much to expect, tho.