BRUSSELS—A pair of terror attacks apparently linked to Islamic State—in Paris and in the skies of Egypt—is forcing a quick recalculation in the West of what more can be done to defeat the militants in Syria and prevent future strikes.

It is possible that the killings of at least 129 people in Paris, along with the apparent terror attack on a Russian airliner, could shuffle the strategic deck and force a change in how Moscow or the U.S.-led coalition plays its hands.

On...