PARIS (AFP) - French presidential frontrunner Emmanuel Macron filed a legal complaint on Thursday (May 4) after his far-right rival Marine Le Pen repeated rumours that he had an offshore account during a particularly bruising TV debate.

The pro-EU centrist Macron and Le Pen battled repeatedly over terrorism, the economy and Europe in Wednesday's TV duel watched by some 16.5 million people.

"I hope that we will not find out that you have an offshore account in the Bahamas," Le Pen said during the debate, which was her last chance to narrow the gap before Sunday's run-off vote.

Macron would win around 60 per cent to Le Pen's 40 per cent if the vote were held now, surveys suggest.

The 39-year-old former economy minister described his rival's insinuation as "defamation" and after his complaint, French prosecutors launched a probe on Thursday into who started the rumour.

Macron's campaign team called it a "textbook case" of "fake news", saying the information began circulating online two hours before the debate started.

The rumour was based on two documents that claimed to show he has an offshore company called "La Providence" in the Caribbean, which his team said included an "outrageous falsification" of Macron's signature.

Macron's team said the information was spread on Twitter by accounts close to Kremlin-friendly news sites like Sputnik and RT, as well as supporters of US President Donald Trump.

Meanwhile, Le Pen's National Front party said her campaign website had been repeatedly targeted by a hacker close to the far-left, who was arrested last week.

The probe into the anti-Macron allegations came as former US president Barack Obama threw his support behind the centrist, saying in a video he "appeals to people's hopes and not their fears".

Obama said Macron had "put forward a vision for the important role that France plays in Europe and around the world" and added "Vive la France!" The day after the debate, in which Le Pen branded Macron "the candidate of the elite" and he called her "the high priestess of fear", the candidates were back at each other's throats.

After the bruising confrontation, a snap poll by French broadcaster BFMTV found that nearly two-thirds of viewers thought Macron was the "most convincing" of the two, broadly mirroring forecasts for the decisive election on Sunday.

"I succeeded in what I set out to do, annoy Mr Macron," she said on a campaign stop in the western town of Dol-de-Bretagne, where protesters threw eggs at her entourage, although she was not hit.

At a final rally in the northern village of Ennemain, the anti-immigration candidate told supporters she would give them back the keys to the Elysee Palace.

"France cannot wait... five more years to hold its head high," she said.

Macron, who headed to the southwestern town of Albi to meet supporters, told France Inter radio: "You can't choke off all of the lies but you can kill off some of them."

At a final rally, he promised cheering supporters: "We will keep our promise of change to the end".

During the visit to Albi, the former economy minister was criticised by some 50 union activists who demanded the abolition of France's controversial 2016 labour reforms.

'BRUTAL AND VIOLENT' DEBATE

The aggressive and often unruly debate shocked many observers used to a more reserved tone in French political discourse.

"It is misleading to call that fist-fight a debate," an editorial in the right-leaning Figaro newspaper said.

Le Monde said it had been "brutal" and "violent from start to finish".

The Elabe poll for BFMTV showed that Macron had convinced 63 per cent of viewers compared to 34 per cent for Le Pen suggested she did little to win over new voters.

Le Pen tried to portray Macron as being soft on Islamic fundamentalism, playing to the concerns of many of her supporters after a string of terror attacks in France.

But Macron was in combative form throughout, repeatedly portraying Le Pen's proposals as simplistic, defeatist or dangerous and targeting her proposals to withdraw France from the euro in particular.

The euro policy "was the big nonsense of Marine Le Pen's programme", he said.

Le Pen called the euro, shared by 19 countries in the European Union and blamed by some in France for a rise in prices, "the currency of bankers, it's not the people's currency".

In the first round of the election on April 23, Marine Le Pen finished second behind Macron with 21.3 per cent after softening the FN's image over the past six years - but without fully removing doubt about the party's core beliefs.

She sees her rise as the consequence of growing right-wing nationalism and a backlash against globalisation reflected in the election of Donald Trump in the United States and Britain's shock vote to leave the European Union.