If the ongoing economic migrant/war refugee crisis is any sign then the EU has a vested interest in all of Africa and the Middle East as they always have. If tinpot dictator starts a war and the EU wants to intervene, carrier battle groups make the projection of force far easier. Especially if you want to avoid having to find a neighboring country to lend you an airstrip and port for logistics to attack their neighbor, even if it's just airstrikes.
Bear in mind it was France that started the intervention in Ghadaffi's suppression of the arab-spring, as well as in Cote d'Ivorie and Mali. If EU/UN peace keepers in Lebanon, the Golan Heights, Sinai, Chad come under attack domestic policy would usually frown on putting lives in the line of fire without the ability to support them.
Don't forget though that carriers and all the ASW helicopters that are usually aboard are vital for ASW warfare. The threat from Russia in the Artic and Atlantic will always be there.
I imagine that an EU army would end up filled with recruits largely like the french foreign legion, which right now is primarily filled with folks from Eastern Europe.
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