Though no more a bad idea than the US dollar from the perspective of the federalists who most strongly supported it. The problem is the union is too weak to force it to work in the way it can in the US.
They tried it before with the Latin Monetary Union. It collapsed for a few reasons, mostly due to the fact that it was a gold and silver standard. I suppose the people who created the Euro thought that the problems with the LMU would be avoided with fiat currency.