They won't fight the Islamists. They'll fight each other. The European Union grows stronger every day, and every day different factions (such as France and Germany) search for ways to ensure that it serves only their interests.
Look for the EU to collapse in Civil War inside 10 years. And don't expect them to be "civilized" about it. It will be interesting to see how many Islamic revolutions take place during the chaos.
I'd wager against that. Seriously, the worst of the EU is too wimpy to even fight. The can't we all get along mentality of the Scandanavian nations is spectacular.
I think the EU might collapse, but it won't be for military reasons.