Considering that it started as a TRADE union and slowly devolved into unified Socialism...they would have been better off staying with separate currencies with each nations central bank set interest rates. I haven't run across one person while I've lived in Europe that likes the Euro. They all long for the individualism of their own historic currency.
The EU was trumpeted at the time as being a trade union, yes, but it didn't take a rocket scientist to figure out at the time that it was very much a political alliance too. Evidence for that lay in the form of the entire EU government coming on line when actual, real, honest-to-God sovereign nations in practice need no "central government".
The EU was the European answer to the American dominance in the global economy, yes, but it was also most definitely a political alliance. It was a tough sell, but in the end the allure of more money and actually being able to compete in the global markets lay right along there with the idea that socialism in a continent infested with socialists would be allowed to spread.
An entire Continent drank the Kool-Aid in the early Nineties. But that isn't all that hard to do for those folks. They're used to it.