The man identified as Rachid Rafaa, 40, has been under house arrest in Morne-Rouge, Martinique, since May 15, 2014, but evaded authorities on Wednesday morning.
News agencies there have reported that Rafaa is of Moroccan descent.
He was arrested back in 2009 and was found with a computer that was the subject of an international arrest warrant issued by Morocco.
He has denied having any connection to the jihadist movement and had said he thinks he is being targeted because of his support for the cause of Western Sahara.
Rafaa claims he was subject to torture for 20 days in his home country, which led him to flee to France.
Martinique officials said he was awaiting extradition back to his home country and could be anywhere at this point.