Barbarin, the archbishop of Lyon in central France since 2002, had been accused of failing to remove a priest from his diocese when he became aware the man had sexually abused young boys 25 years ago.
Barbarin has said he learned in 2007 that the priest, Bernard Preynat, had been accused of sexually abusing Scouts in the past.
Preynat was only charged in January after a victim who was allegedly abused in the 1980s realised in 2015 that the priest was still in service.
Several other victims have also come forward.
Barbarin has said that when he learned of the priest's past he immediately called a meeting with him and when he asked Preynat if he had committed further abuses since 1991 the priest swore he had not.
“You can reproach me for having believed him… but covering up means knowing and letting it happen,” Barbarin said, adding he had “absolutely never” done that.
Prosecutors say Preynat — who was removed from service in 2015 — has admitted the charges.
When complaints were first made against him in the 1980s, he was merely suspended for a few months.
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 despite being aware of his past.
Barbarin has admitted to “errors in the management and nomination of certain priests”.
After the scandal erupted, he in June relieved four priests of their functions over sexual abuse allegations.
The scandal was the worst to hit the Catholic Church in France since 2001, when a bishop was given a three-month suspended jail sentence for failing to inform authorities about a paedophile priest.