Abbé Pierre de Castelet has admitted sexually abusing boys at a Catholic holiday camp he was managing in 1993.
The case came to light when one of the victims, Olivier Savignac, wrote to Orleans's then bishop, André Fort, in 2010 after discovering that Castelet was still being put in charge of holiday camps for children.
Under the guise of medical examinations, Castelet touched his and other boys' genitals, he wrote.
Fort promised to send the abbé for psychological examination and stop him working with young people.
But a year later Savignac found Castelet's name on the list of speakers at a seminar on paedophilia in the church and wrote a letter to Fort's successor, Bishop Jacques Blaquart, who notified prosecutors.
Castelet, who is now 69, confessed when he was questioned in 2012, saying "I did not realise the harm it could do them."
Six men have said that they were abused by Castalet and three of the six are civil plaintiffs in the case.
Bishop in the dock
Fort, who is one of several bishops accused of hushing up abuse by priests, denies knowing that he had a legal obligation to report it to the authorities.
The 83-year-old did not turn up in court on Tuesday because he was "weakened by illness after an operation", according to his lawyer, Benoir de Gaullier.
The presiding judge, Gaëlle Reverter, said she she had been informed he would not be there "in a letter under the door" of her office.
Fort's predecessors, René-Lucien Picandet (1981-1997) and Gérard Daucourt (1998-2002), also knew about the abuse and failed to report it, according to Le Monde newspaper.
The plaintiffs "aren't asking for prison or exorbitant fines", Savignac told La Vie newspaper. "We want legitimacy and recognition of our status as victims so that we can turn the page."
Dealing with the accusations inside the church "leaves the secret of their suffering weighing on the shoulders of the victims", their lawyer, Edmond-Claude Frety said.
In France, as elsewhere, the Catholic church faces a number of accusations of sexual abuse and cover-ups, a situation that has led Pope Francis to issue a letter condemning child sex abuse and efforts to hide it.
The former bishop of Lyon, Cardinal Philippe Barbarin, faces charges for failing to report cases of paedophilia in his diocese.
Bayeux bishop, Pierre Pican, was given a three-month suspended prison sentence in 2001 for not reporting abuse.
On 18 September a priest in Rouen, Jean-Baptiste Sèbe, hanged himself in his church after a woman accused him of inappropriate behaviour towards her adult daughter.
On 20 October Pierre-Yves Fumery, a priest in central France, was found hanged in his presbytery after the opening of an inquiry into "suspicion of sexual assault" on a minor.
The French bishops' conference is set to update its register of sexual abuse this week.
In January 2017 it counted cases against or convictions of 70 of the 15,000 priests and deacons in the country.