They most certainly do, and it is France that wishes to control it. Look how they are attempting to stop Turkey doing maritime exploration. The EU have effectively said they control all the east Mediterranean due to Greece and Cyprus virtually up to the Turkish coastline. Legally this is correct because of the proximity of Greek islands, but in the eyes of the Turks ‘it isn’t fair’ And they wanted to talk it through with Greece. But what happened, France decided to send a couple of Rafale jets and a frigate to the region and stoked up tensions, on behalf of the EU. Turkey is a member of NATO. Greece and Turkey could probably sort this out, with political pressure from EU, USA and U.K.... what it doesn’t need is the EU trying to throw its military weight around. What would happen if the French and Turkey accidentally bumped into each other...there would be chaos, and Russia would then step into the conflict and make political gain.....we have national militaries and we have NATO, what we don’t need is a ham fisted EU military......