The 28-year-old French-Moroccan named as Youssef Ettaoujar was known to police as he was one of the first to be convicted of trying to travel to Syria.
He was arrested on Wednesday on suspicion of plotting "violent acts" against France.
Two men and a woman arrested at the same time have been released without charge, the source added.
In March 2014, Ettaoujar was handed a four-year prison sentence for trying to travel to Syria with two friends. They were the first people convicted in France for attempting to join the jihad in Syria.
Investigators are trying to establish whether he had direct ties to members of IS in Syria, Interior Minister Bernard Cazeneuve said shortly after his arrest.
No weapons were found during the arrests, although an unused Kalashnikov rifle cartridge was discovered.
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