Sapin's admission late Tuesday came in the wake of a scandal which broke the previous day when eight women accused a deputy parliamentary speaker, Denis Baupin, of long-running sexual harassment.
In a statement to AFP, the finance minister said: "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.
"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."
That marks a U-turn from his statements just a few hours earlier when pressed about the incident.
"We are in a place of absolute libel... These are allegations that are totally false," he told reporters.
The incident first surfaced in April, when two other reporters published a book about the corridors of power called "Elysee Off".
The authors, Stephanie Marteau and Aziz Zemouri, claim the unnamed journalist at the World Economic Forum in Davos was bending over to pick up a pen when Sapin said: "Ah, but what are you showing me here" and snapped the elastic of her unintentionally exposed underwear.
The incident had been previously reported -- without giving the minister's name -- as part of a 2015 petition in the Liberation newspaper signed by dozens of female journalists denouncing sexism from male politicians, entitled: "Get your paws off me!"
According to the authors of the book, Sapin's office brushed the incident off at the time, saying: "It was a schoolyard prank and the journalist flew off the handle."
When the book was published in April, Sapin's spokeswoman described the claims as "false and slanderous".
But following the uproar over the allegations against Baupin, there had been renewed pressure for Sapin to come clean about the incident.
Sapin described the allegations against Baupin as "appalling" but said it was up to the judiciary to establish the facts.