[mysto]

A big factor in the creation of the EU was to mitigate against future war AMONG the EU states.
The EU was not created to be a military organization. That's what NATO was designed for. The EU evolved from the common market and the European Economic Community. The key word there is "economic". It was not until later, after the Maastricht Treaty was written, that the French & Germans started talking about a common defense policy for Europe. The EU nations are already fighting among themselves over what this "common defense policy" should be. They can't even agree on Iraq...

[AMDG&BVMH]

Yes, but it is not so much a common (external) defense policy, but a Europe integrated economically, etc., which would make is much less likely for, e.g. France and Germany to go to war with each other again.