Two women were sexually abused by the abbot while in their teens at a church summer camp in the 1970s, the site reveals.
The victims told the Bishop Jean-Louis Papin about the abuse in 2010 and 2016 and the cases were reported to police. But no action was taken because they fell under the statute of limitations, the statement said.
"This conclusion is difficult for the victims of such acts to accept," the bishop commented, "since the consequences are so destrutive for them and those close to them."
The abbot, now 90, took part in ceremonies at Nancy Cathedral and performed other duties until recently but, having admitted to the abuse, has been relieved of his title of canon and asked to take no further part in public ceremonies.
This is the first time the diocese has made such a public statement.
It was made at the request of the second victim, as a way of recognising her "status as a victim", the bishop commented, adding an instruction to church officials to inform him of any reports of sexual abuse and "take the time to listen" to victims or whistleblowers.