My understanding in the US is that the Executive can sign international treaties, and those are not subject ot veto by the Legislative

> In recent decades, presidents have frequently entered the United States into international agreements without the advice and consent of the Senate. These are called "executive agreements." Though not brought before the Senate for approval, executive agreements are still binding on the parties under international law. [0]

An EU law is an international treaty. Can the Senate kick out the US president and refuse to agree to the treaty he signed?

[0] https://www.senate.gov/about/powers-procedures/treaties.htm