Cardinal Philippe Barbarin was named in two investigations of accusations of sexual abuse of children by priests.
Mr Barbarin, one of the highest-ranking figures in the French Catholic Church, is among several church officials accused of failing to report paedophile priests to judicial authorities.
He has denied covering up abuse, but acknowledged some mistakes in handling and appointing priests.
His lawyer, Andre Soulier, said the cardinal is being questioned in Lyon as part of normal proceedings. "He is a witness, and is being questioned as a witness," Mr Soulier said. "We'll see how it goes."
Cardinal Barbarin is being questioned in the case of Bernard Preynat, a priest charged with sexual aggression and rape of a minor and accused of abusing boy scouts in the 1980s.
A Lyon court is scheduled to decide on Thursday whether the case can still be pursued.
Some called for Cardinal Barbarin's resignation after the investigations began, and France's prime minister called on Cardinal Barbarin to take action.
Pope Francis recently expressed support for Cardinal Barbarin, saying he should not resign.
"Based on the information I have, I think in Lyon, Cardinal Barbarin has taken the necessary measures and has taken things well in hand," the Pope said in an interview with French Catholic daily La Croix last month.
Francis has, however, recently laid out internal Vatican procedures to investigate and sanction bishops who bungled handling abuse cases.
The new law, which goes into effect in September, could see a bishop removed from office if the Vatican finds that he caused "grave harm" to his flock by negligently handling an abuse case.
