Organisation is actually pretty good at the battalion level, there's plenty of EU Battlegroups integrating neighbouring armies on a deep level -- or at least making them acquainted with each other. Gotta know the MRE exchange rates. And that's not counting stuff that you mentioned, like the Dutch land army being rolled into German C&C or the German/French brigade.

What's lacking are strategic C&C capabilities on the EU level: There's just too few of them, there should be more cooperation on that level (member states have those kinds of capabilities) which is exactly what the "EU army" thing is about, operationally. Although it has to be said that push come to shove, with so many EU members in NATO, everyone would just re-assign everything NATO to the EU should the NATO fall flat. Armies have scrambled into fighting stances from worse positions.

Macron could lead Europe, yes, but first he has to manage to lead France.