French presidential candidate François Fillon is fighting for his political future as polls show he is likely to be eliminated in the first-round vote by former economy minister Emmanuel Macron.

Fillon, a one-time prime minister who is representing the centre-right, was favourite to become France’s next leader but has seen his chances sink after a scandal over alleged fake jobs for members of his family.

Police continued to investigate allegations that Fillon’s Welsh-born wife, Penelope, and two of his five children were paid €900,000 of public money for work they did not do. Fillon has insisted he will continue his campaign and ask supporters to hold firm until the investigation is finished.

On Friday, Fillon accused “shadowy” forces of seeking to crush him, in what has become known as Penelopegate. “I will hold firm, faced with those in the shadows who are trying to attack me,” he said in a video message to supporters. However, he admitted: “I understand that the accusations are troubling to certain among you because they are pounding … and because of the sums involved.”

Facebook Twitter Pinterest Polls suggest Marine Le Pen could now win the first round presidential vote. Photograph: Eric Piermont/AFP/Getty Images

The latest polls suggested that support for Fillon ha d plummeted in the wake of the allegations.

Pollsters Ifop and BVA both suggest Fillon could be knocked out of the first-round presidential vote in April, with between 18.5% and 20% of support, compared with 25% for the far-right Front National leader Marine Le Pen and 20%-22% for Macron. Benoît Hamon, a surprise choice for the Socialist party candidate, polled 16.5%, and far-left candidate Jean-Luc Mélenchon got 10%. The polls have Macron winning the second round, with a bout 63% against Le Pen’s 37%.

Earlier last week, another poll suggested Le Pen could win the first round with as much as 27%, with Macron in second place with 23%, but that Macron would still win the second round.

Fillon, standing on a conservative and Catholic programme, has faced pressure even from within his own Les Républicains party since the Penelopegate allegations were first revealed in the satirical newspaper Le Canard Enchaîné, and later by the France2 investigations programme, Envoyé Spécial.

A preliminary inquiry into alleged fraud is attempting to establish whether Penelope Fillon worked as a parliamentary assistant . Police searched offices and archives at the National Assembly last week and demanded documents from the Senate, the upper house where Fillon was said to have employed his two eldest children, Marie and Charles.

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Fillon went on television to insist his wife’s job was “real” and “legal”. Last week the couple were questioned separately for several hours by anti-fraud police.

In 2007, I interviewed Penelope Fillon for the Sunday Telegraph. In a video of that interview she can be heard telling me she did “bits and pieces” for her husband, including handing out leaflets and accompanying him on the election trail. But she added: “I have never actually been his assistant or anything like that.”

Envoyé Special was watched by a record 5.4 million viewers when it aired the 10-year-old video on Thursday evening. On his Facebook account, Fillon said the accusations against him were “pure calumny”.

Le Pen is also under investigation for misusing almost €300,000 from European parliament funds to pay the salaries of FN staff, including a personal bodyguard. She has been ordered to repay the money, but is refusing to do so.

On Saturday, Macron launched an attack on Le Pen, saying she was betraying France’s ideals, as the two frontrunners held rallies in the city of Lyon for a weekend of campaigning. On the other side of town, Le Pen was kicking off her own campaign, with pledges to take France out of the eurozone, hold a referendum on EU membership and impose taxes on the job contracts of foreigners.

Opinion polls suggest Macron could easily beat Le Pen in the second round, but faith in pollsters has been shaken after they failed to predict the election of Donald Trump, the US president, or Britain’s vote to leave the European Union last June.

Macron mocked Le Pen’s campaign slogan, “in the name of the people”. “Some today pretend to be talking in the name of the people, but they are just ventriloquists,” he told a crowd of about 8,000 people. “They don’t speak in the name of the people – they speak in the name of their bitterness, they speak for themselves, from father to daughter and daughter to niece,” he said, referring to Le Pen’s father Jean-Marie and niece Marion.

The 39-year-old said Le Pen’s anti-euro, anti-immigrant National Front party would be unfaithful to the French motto of “liberty, equality, fraternity”. “They betray liberty by shrinking our horizons, they betray equality by stating that some are more equal than others, they betray fraternity because they hate the faces that don’t look like theirs,” he said.

Le Pen’s speech envisioned a thriving nation “made in France”, whose citizens would be first in line for state services, and a state unshackled by the “rules-laden” European Union. Immigration, especially by Muslims, would be contained, she said. The French would also guard their own borders, spend francs instead of euros and defend themselves after pulling out of Nato’s integrated command.