Jean-Pierre Ricard issued a statement admitting to the abuse, which he said occurred during his early days as a parish priest.
A French cardinal has admitted to sexually abusing a 14-year-old girl while serving as a parish priest in the 1980s.
Jean-Pierre Ricard, a cardinal since 2006, revealed the abuse in a letter on Monday and announced his resignation from his position.
“Thirty-five years ago, when I was a parish priest, I behaved in a reprehensible way with a young girl aged 14,” he said.
“My behaviour has inevitably led to grave and lasting consequences for this person.”
He went on to ask for forgiveness and said he would be available should the legal and church authorities wish to speak to him.
Cardinal Ricard, 78, was ordained as a priest in 1968. He became archbishop of Bordeaux in 2001 and retired three years ago.
He was also a member of the Vatican Council for the Economy, which oversees all the financial activities of the Holy See.
Eleven bishops or former bishops, including Michel Santier, a former bishop in Creteil, near Paris, are the focus of abuse investigations in France, Eric de Moulins-Beaufort, head of the French bishops’ conference, told a news conference on Monday, at which he also read out Cardinal Ricard’s statement.
The cardinal’s admission is the latest revelations to rock the Catholic Church, which has been embroiled in a global sexual abuse scandal, often involving children, for more than two decades.
In France last year, an independent investigation said French clergy had sexually abused more than 200,000 children in the past 70 years, and its authors said the Catholic Church had turned a blind eye for too long.