On Wednesday, Al Qaeda in the Arabian Peninsula (AQAP), the Yemen-based branch of the terrorist organization, claimed operational and moral responsibility for the "blessed battle of Paris." By "blessed battle," AQAP leader Nasr bin Ali al-Ansi means the cold-blooded murder of 10 satirists and two police officers, plus the long manhunt that ended in the fatalities of Cherif and Said Kouachi, the two French gunmen apparently dispatched by AQAP.

Such a claim seems to demand a response.

You can't ignore a group that brags about ordering the murder of a country's citizens and police, right? Well, the reaction is already beginning. France, like the U.S. after the Sept. 11, 2001, terrorist attacks, is already moving to curtail civil liberties and beef up security laws, and France's lower house voted Tuesday to continue bombing Islamic State — the gunman who carried out last week's other terrorist attack in Paris, on a kosher market, claimed allegiance to ISIS — on a lopsided 488-1 vote.

Bombing ISIS is one thing — Paris is extending a mission already underway, and ISIS probably poses a greater threat to France and its neighbors, since an estimated 3,000 to 5,000 European nationals have traveled to Syria and Iraq to fight with the group. But unpopular French President Francois Hollande may be tempted to expand his country's involvement in the Middle East with a retaliatory, rallly-around-the-Tricolour invasion of Yemen.

He and his government should resist the temptation.

The first reason is obvious: France doesn't need that kind of headache. Yemen is a mess, with a brewing civil war between the Shiite Houthis, who've seized control of the capital, and AQAP and other Sunni factions. The lack of a strong central government has allowed AQAP to run free in large parts of the peninsula — but that just makes Colin Powell's "Pottery Barn rule" (you break it, you own it) all the more relevant and daunting.

France doesn't want to "own" Yemen. The ongoing U.S. military commitments in Afghanistan and Iraq, after more than a decade of war, is certainly one cautionary tale — and France's military is a fraction of the size of America's — but France should remember its own long, bloody experience in Algiers as well.

The second reason is also something France could learn from post-9/11 America: Terrorists want a reaction, and preferably an over-reaction. London-based newspaper editor Abdul Bari Atwan interviewed Osama bin Laden in 1996, and in a 2008 book, The Secret History of al Qaeda, he said bin Laden wanted to lure the U.S. into his web. In 2007, he explained to Tony Jones at Australia's ABC News:

It seems Osama bin Laden had a long-term strategy. He told me personally that he can't go and fight the Americans and their country. But if he manages to provoke them and bring them to the Middle East and to their Muslim worlds, where he can find them or fight them on his own turf, he will actually teach them a lesson. It seems the invasion of Iraq fulfilled Osama bin Laden's wish. [Atwan, to ABC News]

Before France reflexively swats back at al Qaeda in Yemen or elsewhere, it should consider what AQAP really wants. Then it should do what's in the best interests of France.