What's wrong with the President of the Commission? He's the head of nothin' but a bit of bollocks. The Commission is one of the biggest democratical deficits in the EU's system, they even show slight tendencies towards tyranny at time (for instance by trying to pass bills that further fund Euro-wide parties but not Euro-sceptic ones).
Making an army loyal to the undemocratically appointed head of bureaucratic institute would go against everything that makes Europe democratic.
A small force is not possible. Who would command it, when would it react, how would it react? Every nation has sovereignty to react, but every nation is also allied. In case of an attack we would react jointedly anyway. A small strike force would be an offensive means, which makes no sense as we can never agree whether to attack or not.