The political sexism scandal has already prompted one resignation.
Deputy parliament speaker Denis Baupin has himself denied several allegations.
Prosecutors launched an inquiry after eight of Mr Baupin`s former Green Party colleagues said they were subjected to either sexual assault or lewd text messages. The former deputy speaker is suing for defamation.
But the revelations have touched a chord in France, and some 12,000 have signed a petition calling for the mafia-like silence on the issue of sexual violence to be lifted, under the slogan "Levons l`omerta".
When the claims against Mr Baupin first surfaced in two media outlets, several commentators pointed to a book published last month, The Elysee Off, in which the authors described an incident involving Mr Sapin and an unnamed female journalist covering the Davos summit in January 2015.
"Don`t dare pick up a pen in front of him," they warn. According to their version of events, Mr Sapin saw the journalist`s underwear exposed, said "Ah, but what have we here?", and then twanged her knicker elastic.
`I was and remain sorry`
Pressed to respond to the story by reporters on Tuesday, Mr Sapin on two occasions rejected it outright, warning he would take "every action necessary" to defend himself against "inaccurate and libellous allegations".
But late on Tuesday, the finance minister issued a statement to news agency AFP, acknowledging that some sort of encounter happened and that he needed to set the record straight in light of the Baupin affair.
"During a visit in January 2015 to Davos, in the middle of 20 people, I made a comment to a female journalist about her clothing while placing my hand on her back," he said.
"There was no sexist or aggressive intent in my action, but the simple fact that I shocked the person in question shows that these words and actions were inappropriate, and I was and remain sorry."
The journalist had later asked to see him privately to express her anger, he said, and he had apologised profusely. He also said that the woman involved had told him that she considered the matter resolved.
Sexism and harassment in politics have been the subject of great debate in France since presidential hopeful Dominique Strauss-Kahn (DSK) was forced to resign as head of the International Monetary Fund in 2011. The charges were eventually dropped.
A year ago, 40 female journalists signed a manifesto, saying that they had thought the DSK affair had drawn a line under macho attitudes. But they said that sexism existed in all parties and that as long as politics was conducted by men in their sixties, nothing would change.
They referred to the Davos incident, but made no mention of Mr Sapin and gave a less racy version of events.
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