The European Union has no sovereignty of its own. It has none of the inherent jurisdiction of a sovereign state. It is a treaty-based organisation with the 25 sovereign Member States.
The proceedings of the European Court of Justice are principally for judicial review of action or inaction by Member States or Community institutions.
And now -

- you certainly weren't referring to the 'Council of Europe' but to the EU Council (shame on me!)
Of course, you were coreect:
the Council is the main decision-making body of the European Union!
Together with the Parliament it shares the legislative function of the EU.