Earlier this week the girl, from the French city of Grenoble, told her parents via text message that she had been selected to join the jihad war in Syria and had run away from home.
She was detained before boarding a plane bound with a one-way ticket for Istanbul, from where she intended to go to the Syrian border.
Investigators describe her as "heavily indoctrinated" and say that she keeps repeating that she was going to Turkey as a tourist.
After being picked up on Monday, she was placed in the home on Tuesday but managed to run away, only to be caught and returned there.
Anthropologist Dounia Bouzar, author of the book Defusing radical Islam, says the indoctrination of vulnerable teens has increased through the use of social networks and the internet .
In her book , she explains how youth indoctrination linked to Islamism is a growing phenomenon in France
"I’ve been working on indoctrination techniques by radical Islamist for 10 years new," she told RFI. "They used to affect only young and rather fragile people. Today they affect individuals from any social and family environment, people of any religion, atheists, agnostics, whether they practice their religion or not, poor, rich, privileged, educated ... Anyone, really."
About 700 French nationals are believed to have gone to fight in Syria.
Two teenagers were brought back to France from Turkey in January.
"French society and politicians have failed to differentiate sect-like indoctrination and brainwashing by radical Islamists and Islam as a religion," comments Bouzar. "That has led to many errors in appreciation and interpretation which have only been to the religious radicals’ advantage."
The government is drawing up measures to tackle jihadi networks and intends to establish a for families to notify the authorities if their children seem to be becoming radicalised, so that they are prevented from leaving the country without their parents' permission.