* Sarkozy, Obama can claim success from Libya outcome
* Economic fears mask any electoral benefits
By Daniel Flynn and Laura MacInnis
PARIS/VINEYARD HAVEN, Mass., Aug 22 (Reuters) - President Nicolas Sarkozy can present the apparent downfall of Muammar Gaddafi as the result of bold French foreign policy, while U.S. leader Barack Obama may breath a sigh of relief over his going.
Both Obama and Sarkozy, however, could find that any accrued political benefit ahead of elections are likely to be masked by widespread worries over unemployment and a darkening economic outlook.
While Obama deliberately took a back seat in NATO operations against Gaddafi, Sarkozy made a personal gamble in spearheading support for the rebels. As a bombing campaign dragged on, he was anxious to avoid costly military operations running into the start of campaigning for April 2012 presidential election.
"This case illustrates both the strength and weakness of Nicolas Sarkozy's foreign policy, " said Dominique Moisi, an adviser at Paris-based foreign relations think-tank IFRI.
"The strength is intuition, risk-taking and courage. The weakness is a form of improvisation in his methods ... but what will remain, in the end is that Gaddafi has fallen."
"It was even more courageous given that France had no real allies other than the UK, " Moisi said.
The American public is preoccupied with the prospect of a new recession and was never very engaged in the Libya conflict where the United States played a cautious behind-the-scenes role helping NATO air forces halt attacks on civilians.
"The president has had a tough few weeks. Relative to the S&P (credit rating) downgrade it's a plus, but it's far from a vindication of his foreign policy, let alone a vindication of his Libya policy," Duke University professor Peter Feaver said.
Rebel forces fought their way to Tripoli on Sunday, six months after NATO launched an air campaign that cleared a rebel path to the capital. Obama may cite the outcome as endorsement of a strategy, not bold like Sarkozy's but restrained, shaped perhaps by the losses suffered in Iraq and Afghanistan.
"It's pretty clear to the public at large that Obama's heart wasn't really in this effort," said Gary Schmitt of the American Enterprise Institute. "It's awfully hard to crow about something that people know you didn't really want to do to begin with."
BIN LADEN BOUNCE
Obama's previous main foreign policy success has not proved able to blot out negative sentiment about the economy, with unemployment at over 9 percent and the United States suffering an embarrassing downgrade in its credit rating.
The killing of al Qaeda leader Osama bin Laden by U.S. forces in May gave the president only a brief polling boost before concerns about jobs and the budget deficit, and a tough fight with congressional Republicans over the U.S. debt ceiling pulled down his approval ratings through the summer.
A Gallup poll last week found only 26 percent of Americans approved of Obama's handling of the economy, down 11 points since mid-May and by far the lowest of his presidency -- worrying for the White House as the campaign for his re-election in 2012 gets under way.
Most of the credit outside Libya for Gaddafi's departure is likely to go to leaders in Britain and France, who shouldered most of the NATO air strikes backed by intelligence and technical support from the United States.
Jerome Fourquet, deputy director at pollster Ifop, said he believed an end to the Libyan crisis would help erase memories of France's diplomatic hesitation as the Arab Spring began in Tunisia and Egypt.
"After the Ivory Coast, where its military intervention helped install a democratically elected president, Libya shows that France can still play a significant role on the international stage," he said.
Sarkozy, however, continues to trail his Socialist rivals in opinion polls. A survey published by left-leaning daily Liberation showed 47 percent of respondents backed Socialist frontrunner Francois Hollande, 39 percent his party rival Martine Aubry and just 29 percent endorsed Sarkozy, who is widely expected to seek a second term.
While Sarkozy may be able to capitalise on the Libya events to show that his tenacity and commitment paid dividends, many French voters were relatively unconcerned by the conflict.
"International affairs isn't top of their list of priorities," Forquet said.
The announcement on Wednesday of new austerity measures planned for the 2012 budget was, he said, likely to have a much bigger impact on voters concerned about declining purchasing power and unemployment running at more than 9 percent.
Moreover, Gaddafi's removal may not be the end of the Libya conflict, given the fractious rebel leadership and questions over who will run the country.
Duke University's Feaver, who advised the White House during the George W. Bush presidency, warned the trouble in Libya could easily intensify after Gaddafi, much as occurred in Iraq after President Saddam Hussein fell.
"The doctrine that the president invoked that got us into Libya -- the responsibility to protect the Libyan people -- should not let him stand idly by if after the toppling of Gaddafi there is a bloodbath in Tripoli," he said. "It could well be that toppling Gaddafi was the easy part."
(Additional reporting by John Irish and Yann Le Guernigou in Paris, Alister Bull in Washington, editing by Ralph Boulton)