His campaign has been dogged by claims, which he denies, that his wife and two of his children were paid for non-existent parliamentary work.
While an initial investigation is already under way, a decision on a more formal probe has yet to be made.
Francois Fillon told Le Figaro: “I am the candidate and I will continue until victory.
“The closer we get to the date of the election, the more scandalous it would be to deny the Right and the Center of a candidate.”
The first round of the election will be held on April 23, with the second round run-off between two candidates two weeks later.
On January 26, Francois Fillon had told the TF1 channel that “the only thing that would prevent me from being a candidate is if my honor was tainted, if I was placed under examination”.
While France’s financial prosecutor decided to keep an initial investigation open on February 16, the decision to launch a more formal probe would need to be taken by a magistrate. It could take months or years to reach that point.
Media reports say Francois Fillon’s Welsh-born wife Penelope earned €831,400 ($880,000) as her husband’s parliamentary assistant between 1998 and 2012, and questioned how much work she had done.
It subsequently emerged that Francois Fillon had hired two of his children to act as lawyers, paying them €84,000 between 2005 and 2007 – when they were students.
In early February, Francois Fillon said that although what he had done was legal, French people no longer accepted the practice and that he had made a “mistake”.
The controversy has hit Francois Fillon in the polls, with one new survey by Ifop for three French media outlets on February 17 suggesting he is neck-and-neck with centrist candidate Emmanuel Macron.
However, the poll places both behind the far-right’s Marine Le Pen.
Polls indicate Francois Fillon or Emmanuel Macron would easily beat Marine Le Pen in the second round of the election in May.
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