Ariane was last seen at her home, the location of which is currently unknown, in March, but her family believed she may be in Milan as she had friends there.
It was not clear why Italian nor English police ever became involved in the hunt.
The unnamed detective, an Albanian former policeman, asked around after Ariane in Milan and showed people her picture.
Some homeless people said they had seen her sleeping rough, before a hairdresser told him that he had Ariane as a customer and said she was "dirty".
When the detective eventually found Ariane, he summoned her sister to Milan to help her, as she Ariane appeared to have suffered memory loss and confusion.
She was quoted as saying: "I cannot explain... Maybe I was walking, I was assaulted and robbed, and I fell to the ground I hit my head.
"I'm in love with Milan. Residents, passers-by and volunteers offered help but I did not want to... I refused. They gave me food and I was refusing... I was rummaging in bins, trying to eat, I was standing in front of restaurants and hotels so I could eat something."