Barbarin, the archbishop of Lyon in central France since 2002, has 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 spent 10 hours at the police's family protection unit on Wednesday where he was interrogated as part of a preliminary investigation, but has not been taken into custody, his lawyer said.
State prosecutors will now have to decide whether to pursue the case against Barbarin, which has shaken France's Catholic Church.
The diocese of Lyon said in a statement after Wednesday's quizzing that the cardinal would continue to cooperate with the inquiry and that he hoped his testimony would “contribute to the establishment of the truth”.
Barbarin's interrogation comes four days after Pope Francis issued a decree that senior Catholic officials guilty of negligence in child abuse cases can now be dismissed from office.
It was not immediately clear whether the papal decree would affect the Barbarin case.
The pope came under fire for meeting with Barbarin in May and has said it would be “nonsensical and imprudent” to seek the archbishop's resignation at this stage.
Barbarin has said he learned in 2007 that the priest, Bernard Preynat, had been accused of sexually abusing Scouts.
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”.