It is possible to argue for two separate instances of this, but its very much overlapping and full of semantics. You could argue that the Holy Roman Empire was a sort of EU, as while a singular 'empire' it was incredibly decentralized for much of its existence. The HRE was largely made up of nobles who would pay some degree of fealty to a 'elected' Emperor, but otherwise had total control over their own affairs bar a few widespread laws, such as those against Protestantism brought in during the edict of wurms (which didn't work funnily enough)

You could also argue that all of Christendom was a type of European Union, under the kinda-secular-but-not-really, moral and religious control of the Pope and Papacy. You could look at the Crusades and cross-country trade and cultural exchange as examples of this.