After President Obama and French President Nicolas Sarkozy spoke Tuesday morning about NATO disputes over Libya, it was Sarkozy who announced — as Obama flew across South America on Air Force One — that the two leaders had “reached agreement” on the issue.

Since the Libyan crisis began last month, France has repeatedly jumped into the lead: first to recognize the Libyan opposition, first to launch fighter jets over Benghazi, first to call for an international conference about Libya’s future, first to destroy a Libyan warplane in motion.

For the most part, that has suited the Obama White House just fine. Despite some grumbling and eye-rolling over Sarkozy’s grandstanding, the administration has welcomed France’s eagerness to take the spotlight.

It has also suited Sarkozy. According to a poll published this week by France Soir newspaper, two-thirds of the French public approve of the way he has handled Libya, a vote of confidence sure to boost an overall approval rating that had dipped below 30 percent.

Cooperation over Libya has completed the turn away from what one senior French official called “past quarrels,” a reference to the breach in relations over France’s unyielding opposition to the 2003 U.S. invasion of Iraq and the days when French fries were renamed “freedom fries” in the Senate dining room.

Today, the official said, speaking on the condition of anonymity to discuss internal deliberations, “the two countries are shoulder to shoulder,” sharing “common responsibility . . . like after the Second World War.”

French leadership in Libya, he said, does not correspond to a vacuum on the U.S. side, as some Obama critics have charged. Rather, it is a rational division of labor. “Libya is in our back yard, not yours,” the official said, whereas a country such as Bahrain, where anti-government demonstrations have erupted as well, “is very high on the American radar screen.”

The two presidents could not be more different in temperament and the face they present to the world — one cerebral and deliberate, the other overtly enthusiastic and occasionally headstrong.

Both presidents are approaching reelection contests in 2012. But while Obama appears wary of seeming to launch another U.S. military assault in the Arab world and faces an electorate that is weary of the human and financial costs of a decade of war, Sarkozy has been searching for a means to assert leadership on the international stage.

Sarkozy had hoped his presidency of the Group of 20 economic powers this year would provide him with the opportunity to shine. But his agenda for leading a new era of “world governance” had bogged down, and aides told reporters in Paris that he had begun backing away from the bold initiatives he had envisioned.

In addition, Sarkozy’s government was eager to bounce back after a sluggish diplomatic performance during the December and January revolts that led to the downfall of long-standing governments in Tunisia and Egypt. Both were close French allies and partners with Sarkozy in his inconclusive efforts to form a Mediterranean Union as a way to improve relations among Arab and European countries.

His foreign minister was forced to resign after the media reported that she was on vacation at a resort in Tunisia as riots exploded elsewhere in that country and that she had accepted free rides on an executive jet owned by a wealthy businessman close to the ousted Tunisian regime.

Against that background, Sarkozy seized the initiative early in the Libyan crisis, quickly dismissing Libyan leader Moammar Gaddafi as illegitimate. At Sarkozy’s personal prodding, France pushed for 10 days for a U.N. Security Council resolution authorizing international military intervention.

Sarkozy’s leap into the limelight has not pleased everyone. Italy, the former colonial power in Libya, and with extensive economic ties there, pushed long and hard for France to give way to NATO command of the Libya operation. Turkey, which sees France as a longtime impediment to its membership in the European Union, was caustic in its criticism of the French role.

Turkey accused the French of seeing Libya as a future source of “oil, gold mines and underground treasures.” Defense Minister Vecdi Gonul, noting that his government had “difficulty in understanding France’s leading role,” asked this week who had appointed France the “enforcer” of U.N. resolutions regarding Libya.

Germany, with which France has long coordinated its defense, questioned both a NATO role and French leadership.

Britain has been nearly as far out front as France in the operation, but France has seemed to lead the way. Although British Prime Minister David Cameron “has been outspoken” on Libya, “Sarkozy has been better at getting international media attention,” said Stephen Flanagan, who holds the Kissinger Chair at the Washington-based Center for Strategic and International Studies.

Once the dust settles in Libya, “it will be interesting to see the damage this has done” to a common European defense policy, Flanagan said.

While some U.S. lawmakers have accused Obama of failing to move quickly enough in Libya, other experts have decried the image of the United States being dragged too quickly into military involvement by France.

“Inquiring minds want to know what Sarkozy’s motives are for compelling Les Yankees into a full-fledged military involvement in Libya,” Marc Ginsberg, a former U.S. ambassador to Morocco, wrote Thursday on Huffington Post. “Actually, a French-orchestrated Libyan coup d’etat has less to do with Gaddafi and more to do with Sarkozy’s domestic perils as well as France’s incessant jockeying with Germany for European leadership.”