Financially, such a pan european force would be the least bad solution. A fleet of submarines financed by big EU economies, on patrol in the Med, which can already be made very secure and closed off to third party warships when the need arises, and controlled by a board of its financiers, with multinational crews.
Didn't NATO back in the 1960s (With some pushing from McNamara) try something like that in regards to the Polaris SLBM?