French President François Hollande declared the Nov. 13 terrorist attack in Paris an “act of war” by Islamic State, and he was right, if belated, in recognizing that the jihadists have been at war with the West for years. Islamic State, or ISIS, is vowing more attacks in Europe, and so Europe itself—not just France—must get on a war footing, uniting to do whatever it takes militarily to destroy ISIS and its so-called caliphate in Syria and Iraq. Not “contain,” not “degrade”—destroy, period.

But even if ISIS is completely destroyed,...