The EU doesn't have a military or any mandate to put one together under an EU flag. Probably it will happen eventually, but previous attempts to establish one have been rebuffed by the citizens of smaller countries with a policy of neutrality, who still get a veto on questions like this.
Maybe there could have been a combined French/German (or whatever EU countries you'd like...I imagine there'd be no shortage of volunteers in the Baltic) peacekeeping force.
I mean, a UN peacekeeping force would have worked too. A neutral banner instead of NATO, that Putin sees as a direct threat. We don't even need the force to be able to actually fight off a Russian invasion, we just need them to be there to force Russia to declare war on everyone in order to be able invade.
Maybe there could have been a combined French/German (or whatever EU countries you'd like...I imagine there'd be no shortage of volunteers in the Baltic) peacekeeping force.