French Cardinal Jean-Pierre Ricard was among 11 former or current bishops accused of sexual assault, a church body revealed on Monday.
Cardinal Ricard's statement admitting to abuse was read out at a conference of French bishops' in Lourdes, a town in southwestern France.
Archbishop Eric de Moulins-Beaufort, head of the French bishops' conference, said all those accused would face disciplinary action.
Moulins-Beaufort told reporters that bishops were shocked at the cardinal's public statement.
Cardinal says he abused a 14-year-old girl
Ricard said in his statement that "thirty-five years ago, when I was a priest, I behaved in a reprehensible way towards a girl of 14."
"There is no doubt that my behavior caused serious and long-lasting consequences for that person," the cardinal said, adding he had asked for forgiveness from her.
Ricard was bishop of Bordeaux from 2001 until 2019. He said he would withdraw from all functions and be available to church and legal authorities.
Now retired, the cardinal is 78-years-old.
Catholic Church under scrutiny
An independent commission investigating abuse in the French Catholic Church said last year there were thousands of pedophiles in its ranks over many years.
The panel added the French clergy had abused an estimated 330,000 children over the last 70 years.
An investigation in 2020 found that the Catholic Church in England and Wales failed to protect children from sexual abuse throughout the years while protecting alleged perpetrators.