If we're dismissing the impossibility of France and Germany deciding to become one nation after WWII, I guess you could try to POD a stronger movement against nationalism in the years directly after WWII. The most realistic way for this to happen would be a much slower moving federalization of the EU, which would be tricky with UK involvement, and also while de Gaulle is still alive.
This is going to be an unsatisfying answer, but what SUPER EU would look like depends on why it was created in the first place. If it's following some non-nuclear or limited-nuclear WWIII, then maybe it's a Super EU with relatively strong state autonomy and limited federal powers, but fully integrated armed forces. If it's a European Union that slowly federalized, then it would look like something similar to the European Commission that wasn't separate from state sovereignty.
Regardless, unless the POD is the US going off the deep end, there's not much of a reason relations with the US would sour.