They did try. There's the Societas Europaea, a standardized type of corporation largely governed by EU law. It's primarily used by large multinational companies (Think BASF, SAP, Airbus): https://en.wikipedia.org/wiki/Societas_Europaea

That was part of a push to introduce standardized EU-wide legal forms for other types of businesses as well, but the process stalled and never really went anywhere after that.