Europe does need to get it's act together for security quite badly but there are many hurdles in the way, particularity in what the function of a united military will be.
From what I've read on the matter in geopolitical circles;
France wants an EU army that will act as a counterweight to USA but also perform similar interests, so that would mean EU units fighting jihadists in North Africa or far abroad elsewhere, non-state actors, hybrid warfare etc, that is something many others in the EU do not want to be involved in.
Germany is allergic to any military action save a direct attack on Europe by a nation state, Germans anti-military stance is something that has bled into the European project itself given Germany's grip over the EU institutions and bureaucracy. Really the best you could hope from Germany would be to only contribute money and technology & they stay a back seat partner in a unified EU military like some of the smaller member states. Germany at the centre core of an EU military is a terrible idea & a recipe for inaction were the force will have it's hands tied behind it's back then blindfolded.
The Eastern Europeans (Poland and others) are in favor of a unified military but, such a force would be used to discourage Russia or Turkey from getting any ideas and would only be used to protect the EU homeland no far abroad action, but it would also actively repel migrants from the borders (using force), this is something the likes of France/Germany will never agree too (well so long as their political establishments stay in place). Also such an EU army command structure should be in Eastern Europe not Western and to be fair they have a point, any EU military should be kept as far away from Brussels as possible to remain an effective fighting force.
The UK establishment is fundamentally opposed to any EU army and will do whatever it can to undermine this, the UK does not want any hard power in Europe that will eclipse it though that's going to happen anyway given the terminal decline the UK military is in and the British public has no stomach for the funding required to counter that decline. This is why the UK has made defense deals with Poland and is now cozying up to Turkey an increasingly aggressor to Europe.
The UK leaving the EU is a very good thing in this regard as they are one of the major obstacles but will still try to act as a spoiler.
Some of the smaller countries are in favor & others are borderline useless. But then you also have situations like Greece who in the aftermath of the migrant crisis refused to allow EU frontex border patrol agency to operate in Greece citing sovereignty even though they were supposed to be helping secure Greece's own border.
The EU itself, no-one in the security/military space trusts the EU, it is riddled with no borders bleeding heart liberals who care more about rolling out the red carpet then actually defending Europe, at least that's the perception. I'm inclined to agree with that and it would take a lot of initiatives that would require dialing back liberalism in order to win that trust among those who take security seriously.
The Eastern Europeans would be better off forming their own unified military then possibly roping in more friendly countries like Italy & Austria ignoring France/Germany until they can no longer resist on their terms (if they want in).
