The young girl, Océane, went missing on Saturday evening after going to visit a friend in the southern village of Bellegarde, close to Nîmes.
Her body was found in a nearby vineyard on Sunday morning after an extensive search involving police and 300 volunteers.
She had been sexually molested before being suffocated and had also been stabbed four times.
The 25-year-old local man, named Nicolas, walked into the village police station oon Tuesday evening saying he couldn't remember what he had been doing on Saturday evening. He claimed he was drunk and had "blacked out" and asked police to run DNA tests.
Test results confirmed that traces of DNA found on the body of the girl matched the man, named only as Nicolas.
Local newspaper Midi Libre reported on Thursday that the man met Océane as she returned home from a neighbour's house on Saturday evening.
He offered to give her a lift back to her parents' home but instead drove her out of the village where he killed her.
BFM TV reported on Thursday morning that the man, a father of three children, had tried to commit suicide while in custody on Wednesday night.
3,000 people, including the parents of Océane, marched through the village on Wednesday in the girl's memory.
"We will never forget Océane," said the girl's father. "We hope that something this awful never happens again to a child."