By Noah Barkin

BERLIN (Reuters) - It has been a bleak winter for Europe's long-suffering left.

In the span of less than two months, Francois Hollande, Matteo Renzi and Sigmar Gabriel, the center-left leaders of France, Italy and Germany, have all fallen on their swords.

Britain's Labour Party has turned its infighting into a public spectacle. And in Brussels, the left has ceded the presidency of the European Parliament to a conservative, handing the center-right control of the top three EU jobs in Brussels.

But after struggling to articulate a clear vision for the better part of a decade, European leftists may have finally found their savior, a leader who can restore their sense of purpose and, if they play their cards right, halt a dizzying electoral tailspin.

His name is Donald Trump.

No one expects the new U.S. president to change the arc of European politics, which has been bending towards the populist fringes over the past year and away from mainstream parties of both the left and right.

But analysts and officials say Trump's victory - and the defeat of his Democratic rival Hillary Clinton - can teach Europe's left some important lessons and help guide their campaigns at the start of a busy election year in which Dutch, French, German and probably Italian voters will go to the polls.

Both Emmanuel Macron, the 39-year-old former French economy minister who has emerged as a contender for the presidency, and Social Democrat Martin Schulz, who will challenge Germany's Angela Merkel in the autumn, are expected to run campaigns that double down on anti-Trump themes of "Europe" and "values".

"The left needs a narrative and in the current context of Trump and Brexit it can offer an alternative vision," said Henning Meyer, editor of Social Europe and a research associate at the London School of Economics. "If you style yourself as the intellectual opposition to Trump, there is a real opportunity."

LESSONS FOR LEFT

What has gone wrong with the European left?

After the fall of the Berlin Wall and collapse of the Soviet Union killed the socialist dream, center-left politicians such as Tony Blair and Gerhard Schroeder pursued a "third way", ditching ideology for a more transactional kind of politics that accepted neo-liberal economic orthodoxy.

This worked well in the 1990s when times were good. But it became a liability as the new millennium dawned and economic inequalities began to rise, sowing deep divisions within the German SPD, the French Socialists and Britain's Labour Party.

When the global financial crisis hit in 2008/9, voters viewed the left as complicit. Blue-collar workers and jobless younger voters, who saw little difference between mainstream parties on the left and right, began turning to the fringes.

In Austria's presidential run-off election in December, 85 percent of blue-collar workers backed the far-right populist Norbert Hofer. And in the constitutional reform referendum in December that forced Renzi out as Italian prime minister, it was younger voters that helped seal his defeat.

"When the left has been in government, it hasn't been able to fundamentally shift policy in a more leftist, growth- and social-oriented direction," said Italy's Europe minister Sandro Gozi.

Michael Broening of the left-leaning Friedrich Ebert Foundation in Berlin says the center-left in Europe is "fighting for its very survival".

Some officials now say there are lessons from the decline of the past decade that fit well with those emanating from Trump's victory an ocean away.

The first is that authenticity and a compelling narrative count in a world where voters have grown weary of poll-driven politicians who try to please everyone. And second, new faces that can articulate a fresh vision are better than old ones.

A fear of becoming Europe's Hillary Clinton may have convinced the deeply unpopular Hollande not to run for a second term as French president, and Gabriel to make way for Schulz, the former president of the European Parliament who is a relative unknown on the German domestic political scene.

"The lesson for Europe from Trump's victory in the United States is that putting an outsider against the establishment works," said Pascal Lamy, the former president of the World Trade Organisation (WTO) and a top aide to French Socialist Jacques Delors when he was president of the European Commission.

"This is what is giving Macron a lift. He's a new face, younger and fresher than Marine Le Pen or Francois Fillon," Lamy said, referring to the far-right and center-right candidates for the presidency.

Talking up the virtues of Europe and liberal values in an age where nationalism and cultural divisions are spreading may seem like a poor strategy for winning elections.

And while Macron, who is running as an independent, may have a legitimate shot of winning in France, Schulz is expected to struggle to make headway against Merkel, whose conservatives are some 15 points ahead of the SPD in opinion polls.

But anecdotal evidence suggests the SPD will benefit from sending an unabashed pro-European into the race instead of Gabriel, who has a history of bending with the political winds.

In the 48 hours after it chose Schulz, 450 people rushed to join the SPD, the party says. And a poll on Wednesday showed Schulz, a former bookseller who left high school before receiving his diploma, level with Merkel in a hypothetical direct vote for chancellor.

"The left needs a narrative, a vision," said Meyer of Social Europe. "Trump established his authenticity, his relationship with the people, and everything else followed from that. There is a lesson there."

(Reporting by Noah Barkin; Editing by Angus MacSwan)