That’s the French Navy, not the “EU military”. The EU is not a military alliance, there is really no EU military to speak of, just the militaries of member states who may or may not have any intention or capability of aiding others. Like I said, there are about 60 000 “EU soldiers” under the Common Security and Defence Policy, but they’re more for peacekeeping missions.
NATO is pretty much the closest thing there is to an EU military, as a huge percentage of the member states belong to it as well.