Salah Abdeslam has refused to respond to questions from French judges about the November 13, 2015 attacks in which 130 people died at the hands of Islamic State group jihadists.
But in correspondence with an anonymous woman published by the daily newspaper Liberation he appeared "talkative for the first time," the paper said.
"First of all, I'm not afraid of letting anything slip because I'm not ashamed of what I am - and then what worse could be said than what's already been said," Abdeslam wrote, according to the extract from his investigation file.
Abdeslam received messages from a number of correspondents but only replied to one woman, the newspaper wrote.
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The 27-year-old was transferred to France from Belgium in April following his arrest in a police raid in Brussels during which he was shot in the leg.
His two lawyers said in October they would no longer defend him given his refusal to answer questions.
Abdeslam is accused of having provided logistical support to the seven jihadists who died at the various scenes of the terror attacks: the Bataclan concert hall, the Stade de France national stadium, and several bars and restaurants in central Paris.