"Last I checked France was an EU member state and very active in the Centrafricaine Republique, Mali, Libya, pushed for war with Syria, etc. They have been at the forefront of all these interventions."
There was little noticeable intervention in Syria because, like jmo said, the US didn't go with them. Libya was a relatively unique situation for France, given that they were just a thin waterway away, and Mali was a terrorist group. I'm not up to date on the situation in CAR but if it involves the LRA in any way then it is a conflict worth having.
No one said the EU are passive onlookers. They simply aren't about to start a war with Russia, who would spank their collective asses if they fought without the US, and even with the US in a WW3-esque scenario, it would be a toss-up, which isn't the EU's type of fight (as I made mention of before).