Airbus was not related to EU (or EEC). It was basically a France-Germany bipartite cooperation, with tiny bits of Spain and Netherlands, and UK being in/out. UK didn't belong to EEC when they were supposed to take part in the beginning of the project. Spain didn't join EEC until 20 years later. Netherlands were in by accident, in a way.
While Airbus is older than the current EU it was and is a multi-national cooperation in the same spirit, where political and national interests need to be taken into account, even if it reduces economic efficiency. They even needed the Beluga https://en.m.wikipedia.org/wiki/Airbus_Beluga because they could not concentrate manufacturing of big parts in a single country.
Boeing should have a clear advantage because they have no such political interference. But it doesn't seem to have prevented Airbus from being a serious competitor. Whether the political interference is older than the EU or from the EU of today should not make a significant difference here.
