Cardinal Philippe Barbarin said he was "obliged to assume all the evil committed by some priests and personally apologise for the damage they have caused by sexually abusing children."
He said he apologised even though he was not in power in the diocese "when the abominable acts took place".
Barbarin, 65, said he met Wednesday with priests, deacons and members of the community in the eastern city of Lyon to discuss a case which even prompted the government to weigh in.
Barbarin has been caught up in a scandal over abuses that took place 25 years ago, long before he became archbishop of Lyon in 2002.
A priest in his diocese, Bernard Preynat, was charged in January after victims came forward with claims he had sexually abused Scouts between 1986 and 1991.
Prosecutors say Preynat has admitted the charges.
The victims have filed complaints against several senior diocesan officials, including Barbarin, accusing them of failing to report the priest or remove him from duty.
Barbarin said that when he learned of the priest's past in 2007, he asked him if he had committed further abuses since 1991 and the priest swore he had not. Barbarin said no accusations had been made since.
"You can reproach me for having believed him... but covering up means knowing and letting it happen. Absolutely never," he said.
Barbarin has since faced other accusations of failing to remove two other priests in his diocese who had histories of sexual abuse.
"I have never, never, never covered up acts of paedophilia," Barbarin said last week after Prime Minister Manuel Valls urged him to "take responsibility" in the case.
The scandal has been extremely embarrassing for the Catholic Church in France, which has worked to harden its stance against predator priests since Pierre Pican, bishop of the Normandy town of Bayeux, was convicted in 2001 for failing to report abuse.
Catholic church under attack
The Church continues to be dogged by cases of paedophile priests and past cover-ups, despite Pope Francis' promise of a crackdown.
The case recalls the recent Oscar-winning film "Spotlight", which highlighted how the Church would transfer deviant priests between parishes in Boston in the United States, and protected clergy from prosecution.
While this practice is no longer commonplace, the French case raises the question of how deep Church authorities should dig into abuse cases lurking in their past.
"I know what must be done on current cases. But what to do with these old cases?" Barbarin asked last week.
The Vatican has backed the cardinal, saying he had shown "a great deal of responsibility".