I view it like this... I'm sure many will say I'm wrong, but here we go...
After the collapse of the USSR, there is no balance of power against the United States in the affairs of the world. We are the ONLY superpower left, and people feel threatened by that.
The EU is merely attempting to restore a balance that was lost. I don't feel threatened by it (at the moment), nor do I feel the EU is attempting to strengthen Europe for a possible war against the United States.
I feel that they are attempting to consolidate the limited resources of each of the European Countries as individuals into a cohesive whole that can compete with the United States on a global level economically, not militarily.
There is obvious potential for future problems as always, but at the moment I don't think their goal is to build a unified alliance capable of waging war against the United States.
Just my opinion