By Michel Rose and Marine Pennetier

PARIS (Reuters) - A new chapter opened in France's closely contested presidential election campaign on Sunday as Socialists voted to choose their champion and conservatives fought to keep their scandal-hit campaign on track.

Polling opened at 0800 GMT in a primary runoff that pits pro-business ex-prime minister Manuel Valls against hard-left lawmaker Benoit Hamon for the Socialist ticket. A result was expected by the end of Sunday.

Francois Fillon - chosen as conservative candidate last year by his party The Republicans but hurt last week by a newspaper claim that his wife was paid for fake work - was meanwhile due to hold a rally on the outskirts of Paris.

Hamon is favourite to beat Valls in the Socialist primary's head-to-head vote, even though the outcome remains uncertain given that any voter can take part.

By midday, the high turnout Valls has been calling for looked likely, with over half a million people taking part by midday, according to the organisers, up from around 400,000 in last week's first round.

Neither man has much chance of winning the presidential race itself, though, after five years of unpopular Socialist rule.

Until Fillon tripped up over his British wife Penelope's pay, prompting the opening of an official inquiry into the matter, he was favourite to move into the Elysee presidential palace.

Opinion polls showed him beating far-right National Front (FN) leader Marine Le Pen in a run-off vote on May 7 with a comfortable two-thirds of the vote.

Popularity polls since have shown his rating slip slightly, although there have been no polls on voting intentions since the scandal broke.

Whichever Socialist wins on Sunday, opinion polls show the party destined for a humiliating fifth place in the April 23 first round of the election itself, behind Fillon, Le Pen, centrist Emmanuel Macron, and the far left's Jean-Luc Melenchon.

Nevertheless, Sunday's outcome is important to the election, and for the future of the Socialist party, unpopular after five years of high unemployment under President Francois Hollande and split by a pro-business policy u-turn that angered its left-wingers.

Hamon is one of those leftwingers. He wants to give a "universal income" to all citizens at a cost of 350 billion euros and impose a tax on robots.

Analysts say that if he wins the ticket, that would boost Macron's chances of the presidency, potentially pushing Valls' centre-left pro-business supporters into former investment banker Macron's arms.

It could also hasten a break-up of the Socialist party, analysts say.

Macron, Valls' economy minister until he quit last year to launch his presidential campaign, has spurned the Socialist primaries and is standing instead for his own centrist political movement.

The latest polls show him breathing down the necks of Fillon and Le Pen.

FILLON ON OFFENSIVE

Fillon sought to get his campaign back on track on Sunday with an interview in the Journal du Dimanche newspaper.

Muck-racking against mainstream candidates could end up propelling Le Pen into power, he said.

"If we continue to try to destroy credible candidates in the presidential election, this is how it'll end," Fillon told the paper.

It was the satirical weekly Le Canard Enchaine that threw his campaign off track last week.

Its report said Fillon's wife had received a total of around 600,000 euros ($640,000) for employment by him and his successor in parliament, and later as a literary reviewer for a cultural journal.

Fillon, who says that as president he would slash public sector jobs and tax on companies, has not denied the figures, but he has denied the jobs were fake, saying his wife for years proof-read his speeches and prepared press reviews.

He has said he would not give up his presidential bid unless he was himself put under formal investigation. It is unclear who would replace him in that case.

Last week, investigators searched the headquarters of the cultural journal that employed Penelope Fillon. They also seized files on Francois Fillon held by France's official anti-corruption watchdog.

(Editing by Andrew Callus and Raissa Kasolowsky)