Really the usefulness of a Eurocorps is a big question. If you need a deployment somewhere, you could just have some unit from some army tapped to do it just easy.
Political union is a huge problem because though some people may not realize it, Europe is a very diverse place. Any union would be a Confederation of the loosest sense. Plus the UK's stance on it would be uncertain.
And also from what I've seen anyways, I can't really see France and Germany forming a stable long term relationship that doesn't require America Bashing. Not to mention Holland vs Germany. That stuff is brutal. Also Walloons vs the Flemish in Belgium alone. Of course the Basques and their issues.
Complicated, complicated place.