In a "worst" case scenario we are talking about - maybe - 3 or 4 future EU (British and French) "heavy" aircraft carriers capable of carrying 40-50 airplanes. Plus the Spanish "Juan Carlos I" capable of carrying around 30 airplanes in its carrier configuration. Plus 2-3 light carriers carrying 8-10 airplanes each.

That´s not comparable to 12 US aircraft carriers capable of carrying 80-90 airplanes each. Not to mention that the EU simply doesn´t have the world-wide bases like the USA.

Simply put, if the EU - disregard the UK ties to the USA here - wanted "to cause mischief" on its own it could maybe deploy the equivalent of 1-2 US aircraft carriers. Plus maybe in a best case 10000-12000 soldiers and their equipment in their amphibious ships.

You can´t invade and secure a country with 12000 soldiers and maybe 100 - 200 airplanes. Won´t work unless its Monaco or Andorra. :)