Three young people came forward with allegations referring to the 57 year old Bishop of Dax, Herve Gaschignard, but none of them concerned paedophilia, the Church said.
Archbishop of Bordeaux Jean-Pierre Richard was quoted by AFP as saying: "His behaviour upset and troubled a certain number of these young people, who spoke to their families about it."
A 14 year old claimed Gaschingnard asked about his sexual habits, while a 14 year old girl come forward to say he stroked her thigh and whispered "inappropriate" things to her.
Archbishop Jean-Pierre said two church workers reported concerns about Gaschingnard on 21st March, prompting the Vatican to responding by asking that the bishop tender his resignation.
According to the Catholic newspaper, La Croix, concern was previously raised over Gaschingnard's behaviour in 2011, when he was serving as an auxiliary bishop in nearby Toulouse.
"No complaint has been lodged" with local prosecutors, Dax diocese was reported by AFP as saying.
The Vatican's intervention - within weeks of being made aware of the concerns - arguably marks a speed of response it has been accused of not showing in previous cases.