The former prime minister called a news conference to address the scandal that broke two weeks ago.
It's alleged that the 62 year-old paid his wife and two of his children for parliamentary work that didn't exist.
Members of his own centre-right party, The Republicans, have urged him to quit the race to give the party time to find a replacement candidate.
However Mr Fillon says he will not withdraw from the election and denies any wrongdoing.
"Yes, I employed my wife as an employee. She then worked for my replacement member of parliament. And then she became my parlimentary assistant again later on. She occupied this position for 15 years altogether and she was paid, on average on a monthly basis, 3,677 euros net per month. A perfectly justifiable salary for a person that is a graduate of arts and law."
But he has conceded he made a mistake.
"Working with your family in politics is a practice the French now reject. What was acceptable in the past is no longer accepted today. By working with my wife and my children, I gave priority to a relationship of trust which today is called into question. It was a mistake, I deeply regret having made this mistake, and I would like to apologise to the French citizens."
Fraud police are investigating the incident with the results possibly adding another blow to his campaign.
Mr Fillon faces a tough challenge to the presidency.
Prior to the scandal surfacing two weeks ago, opinion polls showed he was the clear favourite to win the election.
His apology also comes days after far-right candidate Marine Le Pen launched her bid to run for president.
Ms Le Pen is riding on the wave of populism sweeping Europe, and also led to the election of Donald Trump in the United States as president.
She launched her campaign rallying against globalisation and what she called Islamic fundamentalism.
Renaud Girard is a the chief foreign correspondent for Le Figaro newspaper.
Speaking to Al Jazeera, Mr Girard says she is an appealing candidate for many French people.
"She's quite popular now because there's kind of a rejection of the whole system, all politicians, and she has never been or her party has never been in power. She's also softening her position - she said she would choose a prime minister who is not from her party and that she would make a government of national union with all 'the patriots', the people who like France like her, she said."
But he says it will be difficult for Ms Le Pen to achieve victory.
"The French system is not like the American system. There are two rounds of election and you really need more than 50 per cent of the popular vote to become the president. Yes, she's like Donald Trump, an outsider. She doesn't belong to what she calls the system but she for the time being, she lacks an ally on the right. She's far right, she lacks an ally on the right."
But perhaps the candidate likely to clinch the ballot is independent Emmanuel Macron.
The former economy minister has seen a surge in popularity with his centrist agenda.
Opinion polls suggest the 39 year-old will reach the election's crucial second round run-off in May and defeat Marine Le Pen by a comfortable margin.
Irish Times Paris correspondent Lara Marlowe, says the popularity of Ms Le Pen and Mr Macron appears to be a rejection of establishment political parties.
"The socialists are completely divided. They're really splitting. So the two parties that look best poised to win the presidential election are the Front National, the extreme right wing national front, and a Emmanuel Macron group called En Marche! which didn't even exist a year ago. So it's quite extraordinary to have these two parties, the National Front which were really pariahs until quite recently. And En Marche! which has just been invented out of nowhere really in the forefront of French politics and stronger than the two traditionally strong parties."
France goes to the polls in April.
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