Which EU body is not elected? The European Parliament is directly elected by the people. The Council consists of each member states elected governments. The Commission could be considered not elected, but everyone involved in choosing it is ultimately elected, either directly or indirectly. It also cant make laws without the approval of the unambiguously elected bodies.

The parliament definitely does have constituents, and they needed to approve this for it to get through (the rest of the bodies are either controlled by the parliament or by the individual governments of the EU members).

Legislative power is co-held by the parliament and the council: the parliament is directly elected by the people and the council is elected by the governments that were elected by the people.