NATO was, and remains, a defensively based alliance of individual sovereign states. The "European Army" is a political creation of those who plan the ever closer union of EU member states. There is nothing logical about it. Nonetheless many believe such closer union to be logical and a guarantor of future peace in Europe.
I would respectfully suggest that they are greatly in error. Once that unity leads to total power at the centre, at the cost of the sovereignty of constituent states, then you have all the makings of future conflict. The world has been here before, many times. Are we forever to repeat history rather than to learn from it?
NATO kept the peace in Europe, not the EU or its many other manifestations, mainly through the existence of Article 5 of the Treaty. That restriction would scarcely apply if NATO were replaced by a European Army threatening the suppression of a would be secessionist state. Hence are the bitterest of all wars started, ie civil wars.