I doubt there's much redundancy - rather I would say the EU lacks certain things it needs as a larger Great Power - too few Aircraft Carriers, for one.
While it might be a goal for a unified EU bloc to project power, it is not a mainstream goal to project power against the United States. You don't need many aircraft carriers unless you are interested in challenging the USA.

The Continent, North Africa, West Asia, and <Anglo-French> former colonies ought to be managed without extensive naval buildup. Especially if you count out British interests - you can see to yourselves on that end, right?