No. Here is the list of organizations that have the power to make laws in the EU (and JUST the across-the-EU part of that list, within countries, within states, within provinces, within towns there's another list). This is referred to in legal tradition as the "Hierarchy of norms", because there is also a clear order defined.

https://eur-lex.europa.eu/EN/legal-content/glossary/eu-hiera...