But while the French and British moves are an important political signal in support of an ally, they can hardly be expected to be a game changer on the battlefield.
ISIS cannot be defeated through a bombing campaign alone.
Airstrikes can degrade the group, but ultimately ground forces will be needed to defeat ISIS, both in Iraq and Syria.
At this point, it is highly unlikely the Western-backed Syrian opposition could field the necessary army. The training and equipping of this force has been entirely inadequate, and it is too fragmented politically.
Western nations do not have the political will or military capability to undertake a protracted land operation with the required numbers, and such an effort would risk serious backlash regardless of "good intentions."
A coalition of Middle East states is also unfeasible given their differing agendas and lack of combat experience.
No perfect option
The most viable candidates to be the boots in the sand facing ISIS are Bashar al-Assad's Syrian army forces, the Kurdish Pershmerga and the military forces of Iraq.
However, none of these forces is being properly empowered because the anti-ISIS coalition -- the Western countries in particular -- are uncertain of the geopolitical ends they are seeking.
Assad's forces can't be supported without compromising democracy. The Kurds can't be supported without angering Turkey, and the Iraqi military cannot be supported without buoying Shia power over the Sunni minority in Iraq.
There are a legion of political decisions that must be made before military action can be effective. The place of the Kurds in the Middle East must be determined. The future of the Assad regime in Syria needs to be agreed upon. Most importantly, rapprochement between the Sunnis and Shiites in Iraq and across the Middle East needs to be advanced.
All this is vital because only once the political goal is decided upon will it at last be feasible to develop the military means to achieve those ends.
It is ill-advised to have only the goal of eliminating ISIS and leaving a vacuum.
No doubt, all of this will require a huge political effort, but it must be undertaken with as much visibility as the current bombing.
Air power supporting ground troops
Once an end state is determined, airstrikes will be much more effective because they can be undertaken in support of ground forces. Troops will be able to advance on the battlefield first and then take advantage of the strategic effects of bombing.
This dynamic of Western air power supporting local proxy armies was responsible for success in both Kosovo and Afghanistan.
As part of this air campaign, it will also be vital that special forces be present on the ground providing forward air control and advising. This will entail some risk, as will providing close air support with rotary-wing assets and intelligence assets. However, large numbers of outside forces will not be required.
At this point, if there is any success against ISIS, it is likely to be dictated by Russia despite the shooting down of a Russian jet by Turkey
This is because by siding with Assad, Russian President Vladimir Putin has a proxy ground army with which Russia can cooperate to advance on the battlefield. Already this approach is seeing some results, albeit at a humanitarian and military cost.
Unity or chaos
However, any success is likely to be limited unless the vast anti-ISIS coalition comes together with a common objective. If there is no unity of action, the region will remain chaotic and at the mercy of force of arms. It is in this context that groups such as ISIS thrive.
But of course the military cannot rest while political negotiations are working out the future for the region.
So what can be done in the interim? The correct approach was identified by T.E. Lawrence almost a century ago. He noted that "standing still" in an "irregular war, was the prelude to disaster."
ISIS feeds on chaos, and thus the key is not to overreact and cause more chaos. The U.S. 9/11 Commission noted that Osama bin Laden wanted the United States to overreact to the al Qaeda attacks on New York and Washington.
There is a high probability that ISIS is hoping for the same response to the attack on Paris. Instead, the military strategy should focus on ensuring ISIS forces stand still.
Here is where the airstrikes have been effective and can continue to be for a time. They have not turned ISIS around, but the group's blitzkrieg has ended, and it has stagnated.
If this can be maintained, it could provide time for political solutions to be sought, which will be the prelude to an effective counterattack.