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7 year oldHe has become mired in a scandal surrounding claims that his Welsh-born wife, Penelope, was paid large sums over a number of years for "fake jobs".
Mr Fillon has denied any wrongdoing.
He has faced mounting pressure to quit the presidential race.
Investigators are now expected to look into payments of more than €80,000 (£69,000; $86,000) made to Marie and Charles Fillon, when their father was a senator between 2005 and 2007, reports said.
Mr Fillon, 62, said his children were paid as lawyers, for specific tasks. But neither was a qualified lawyer at the time. According to satirical weekly Le Canard Enchaine, they drew pay cheques not for assignments, but for two full-time jobs.
The newspaper earlier alleged that Penelope Fillon was paid hundreds of thousands of euros for work she may not have done. The couple have said she was legitimately employed as his parliamentary aide.
But putting more pressure on Mr Fillion, France Televisions said it would screen extracts from an interview with his wife in 2007 in which she told British media that she never worked as his assistant.
Mr Fillon said he would fight the accusations "to the end".
Recently the favourite to win the presidency in elections in April and May, Mr Fillon has now slipped behind far-right leader Marine Le Pen and centrist Emmanuel Macron.
An MP from his Republicans party told RMC radio that an open letter was being drawn up by some members calling for him to be replaced by his 71-year-old rival Alain Juppe if he decides to stand aside.
But Republicans lawmakers who support him published their own letter, denouncing what they called an "attempt to kill" his candidacy.
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