PARIS, Nov 27 (Reuters) - Francois Fillon, a socially conservative free-marketeer, won France’s center-right presidential primaries on Sunday, setting up a likely showdown next year with far-right leader Marine Le Pen that the pollsters expect him to win.

With votes from four-fifths of 10,228 polling stations counted, Fillon, who went into Sunday’s second-round run-off as firm favorite, had won over 67 percent of the vote in a head-to-head battle with another ex-prime minister, Alain Juppe.

“I must now convince the whole country our project is the only one that can lift us up,” a visibly moved Fillon said at his campaign headquarters after Juppe conceded defeat.

All eyes now turn to the ruling Socialist party and to whether the deeply unpopular President Francois Hollande will decide to run for the left-wing ticket in his party’s primaries in January, amid signs that his prime minister, Manuel Valls, is considering a bid of his own.

France, the euro zone’s second largest economy, has faced stubbornly high unemployment under Hollande, and the past two years of his term have been marked by Islamist militant attacks that have killed 230 people and focused attention on immigration and security concerns too.

Opinion polls suggest neither he nor any left-wing candidate would make the second round of the presidential election itself next May, leaving Fillon a clear run at the anti-EU, anti-immigration National Front leader Le Pen that the surveys predict him to win.

Polls elsewhere have nevertheless recently proven out of step with the voting patterns that saw Britain vote to leave the European Union and Americans elect Donald Trump as president.

Next year’s French presidentials are shaping up to be another test of anti-establishment anger in Western countries.

Fillon, 62, came from behind in opinion polls over the past two weeks.

In last week’s first round Les Republicains party primary he knocked out former president Nicolas Sarkozy, under whom he served as prime minister from 2007 to 2012, and pushed Juppe into second place.

A racing car enthusiast who lives in a Loire valley chateau, Fillon promises radical reforms to France’s regulation-encumbered economy, vowing to roll back the state and slash government’s bloated costs.

The Socialist primaries are due to take place in January. Hollande has two weeks in which to decide whether to take part and run for re-election.

Sunday’s Les Republicains primary victory for Fillon and his hardline economic platform give the 62-year-old Hollande a target to attack and could convince him to make a bid for a second five-year mandate against the odds.

Fillon outflanked Juppe and Sarkozy after a campaign in which Juppe emerged looking soft and pandering to the left, and Sarkozy’s rhetoric steered too close to extremism for some.

Enthusiastic for free-market principles in a country where state interference is the norm for governments of all political hues, Fillon is a rare fan of the late British Prime Minister Margaret Thatcher.

He is from France’s conservative Catholic right, has misgivings about gay marriage, and believes immigrants should assimilate to French cultural values.

Juppe called for all factions to now come together. “I congratulate Francois Fillon,” he told supporters. “To victory next year.”

Sarkozy also called for unity.

“The moment has now arrived for our political family to rally together around Francois Fillon in order to guarantee that France gets the alternative to the current policies that it needs more than ever before in 2017,” he said in a statement.

(Additional reporting by Sudip Kar-Gupta; Writing by Andrew Callus, editing by David Evans)