François Fillon clung to his place as France’s conservative presidential candidate on Friday amid worsening opinion poll ratings and speculation about his ability to carry on after accusations his wife got public money for work she did not do.

Police carried out searches at the Senate in connection with the fake job allegations on Friday, looking in particular for information concerning payments there to Charles and Marie, two of Fillon’s children, the public prosecutor said.

Senate President Gerard Larcher, named by some politicians as a desirable substitute if Fillon bowed out, took to Twitter to deny a report in news publication L’Obs that he was about to withdraw his support for the current presidential contender.

People in his own camp discussed other options as a second poll in two days showed a large majority of voters believed the former prime minister should pull out of the election, a two-round contest that opens on 23 April.

The 62-year-old vowed at a Thursday night rally in northeast France to fight what he called a “demolition exercise”, telling a crowd of around 1,000: “People are not seeking justice. They are seeking to destroy me, and beyond me to destroy the Right and steal an election.”

Until the scandal over payments to his wife and two of his children surfaced last week, Fillon was enjoying what looked like a nearly unassailable lead over other presidential contenders, ahead of far-right National Front leader Marine Le Pen and independent centrist Emmanuel Macron.

An Odoxa poll for franceinfo radio showed 61 per cent believe Fillon is now wrong to persevere in his presidential bid.

Sniping from his own right-wing political camp continued, primarily from politicians connected to party grandees he beat to win the presidential ticket of the Republicans party.

“A million euros is no small sum,” said Rachida Dati, who was justice minister under Nicolas Sarkozy, president from 2007 to 2012 but third-place loser in the contest that handed Fillon the Republicans presidential ticket.

She dismissed two other names cited as possible replacements if Fillon pulled out – Alain Juppe and Sarkozy.

They were both also-rans in the primary that Fillon won last November. But Juppe has the handicap of a court conviction more than 10 years ago for misusing political funds to finance phantom jobs for political friends. Sarkozy is being pursued by investigators on suspicion of illicit campaign financing.

Fillon has denied any wrongdoing since Le Canard enchaine, a muckraking satirical weekly, last week accused him of paying his British wife, Penelope, hundreds of thousands of euros for work as an assistant that she appeared not to have done.

That scandal, subject of an official inquiry, has broadened since then with further reports by the newspaper of payments 10 years ago to children Marie and Charles, who are now lawyers in their thirties. On Thursday, a prime-time TV programme broadcast a decade-old interview in which Fillon’s wife appeared to say she had no role as an employed assistant.

“I have never actually been his assistant or anything like that. I don’t deal with his communication,” she said in that interview with The Daily Telegraph.

Fillon had presented himself as a clean-cut, clean-living candidate. Welsh-born Penelope has long shunned the limelight for what, in rare comments to the media, she calls a country life as mother of four at the family manor an hour or two by car west of Paris.

Opinion polls have shown Fillon stumbling to level with rival Macron. Whichever of the two makes it to the 7 May runoff round is expected to face Le Pen, and beat her convincingly.

Should he bow out, other names that politicians have shared with journalists as replacement contenders are Senate president Larcher, publicly proposed by right-winger Christine Boutin on Thursday, and ex-ministers Xavier Bertrand and François Baroin.