According to a source close to the enquiry, the man -- whose name was not given but who was known to the authorities for being radicalised – was arrested near the northern city of Lille.
Paris prosecutors have opened an inquiry on grounds of terrorist conspiracy.
The suspect is believed to be connected to Akim and Khalid Saouti, two brothers who were charged in Brussels on Wednesday with belonging to a "terrorist group" and were believed to be planning an attack with a large stash of weapons including Kalashnikov rifles.
The pair, who were arrested the previous night in the Brussels suburb of Anderlecht, are brothers of convicted jihadist Said Saouti, a member of the Kamikaze Riders, a notorious bikers' club based in Brussels.
Last year, Saouti was jailed for six years for recruiting people to jihadist organisations and supporting the Islamic State (Isis) group on social media.
The French suspect has been jailed four times for acts of violence and theft and was put under surveillance after leaving prison in May 2015 where he was believed to have been radicalised.
He was then observed making several trips to Belgium, where he met the Saouti brothers with all of them seen handling bags at a garage in Anderlecht.
"The fear of an imminent attack in France or Belgium led to a wave of arrests," a source close to the probe said, referring to last week's raids.
Inside the garage, they found a box containing three Kalashnikov rifles, a pump-action shotgun, three handguns, four detonators and ammunition as well as uniforms from the police, the security forces and the emergency services.
One of the bags they were seen handling was found at the French suspect's home, containing several kilos of jewels, the source said. Investigators also found jihadist propaganda and footage of suicide attacks on his computer.
Investigators from a joint Franco-Belgian operation had on Wednesday confirmed arresting a 42-year-old man just outside Lille on suspicion of links to the Kamikaze Riders who was planning a "violent attack".