Economic and monetary union is as a group of policies aimed at CONVERGING the economies. From your link.

The European Union consists of 27 countries.

25% of them did not adopt Euro as the currency.

"common" language is orthogonal here - it would be valid if you could legally use euro everywhere. You can't, it's not a currency in the quarter of the states. Sure, someone may accept it and offer you the exchange to the local currency.

Vatican City example is also not very good (to put it mildly), because Catholicism is a state religion. You're not going to be deported for being Sikh, yes, but it's akin to the Romanian not being deported form Portugal for carrying lei in his pocket.

Euro is NOT a common currency in the EU. It is by far the most popular. It is a common currency in the Eurozone countries. And these two are distinct from Europe as well.

I'd suggest you discuss your ideas with someone before posting them again.