Why would an organisation founded on "the respect for human dignity, freedom, democracy, equality, the rule of law, and respect for human rights" need an Army? To defend itself from outside threats? It already has that in the form of NATO, for which it has a thinly disguised contempt. To defend itself from internal insurrection? Far more likely, and if the UK and USA have any sense they won't have any part in it.
Union Armies are there for one principal reason, to protect and defend the Union against threats from within. I imagine we will be seeing an ever increasing number of those arising as Le Grand Projet moves inexorably onwards to an ever closer unity.