Actually, the first signs that war will be coming, will probably be the revitalization of their military forces. They wont make these initial investment shifts very public though. That seems to be the historic norm for the Euro continent, but this situation is unique in the aspect of Muslim immigration. The internal civil war could go hot very quickly due to something completely out of control of the ruling corrupt oligarchies.
That brings up a different military theory, which may be of some interest.
The idea of mass standing armies has only been around effectively since the age of Napoleon. Before then, a national call up was a short term, haphazard affair with any logistics provided by wealthy royals. So for the most part, mercenaries were the preferred means of fighting smaller wars.
And oddly enough, by being far less expensive than paying for a standing army, mercenary companies will likely be the future, not just for Europe, but they could be very useful for America as well.
In our case, we have a top of the line, highly trained and equipped military, that has become very overextended on minor missions such as peacekeeping and disaster relief. Forces scattered in 100 nations around the world, when they only need to be in perhaps a dozen.
Mercenaries could perform all sorts of low level functions (as well as being deployed to places we prefer not to go, like Africa), and save the US literally billions of dollars that could be used to keep our military in top shape, for real missions, where their skills and equipment are vital.
As far as Europe goes, they just cannot afford standing armies anymore. But being defenseless can be a drag. Yet the rules of having mercenary forces like the French Foreign Legion are well known (must be offshore, must have regular officers in charge, and must have logistics and transport provided by the regular military).
In the US, Xe Corporation (fmr Blackwater), is extremely profitable because the US government has no end of things it could do, and even with good pay and profits, it only costs a fraction of an equivalent military unit.