Zuhair Mohamad Hassan Khalid al-Abassi, alias "Amjad Atta", was one of three men for whom France issued an international arrest warrant earlier this year.
Overall, between three and five men are thought to have taken part in the attack, which was blamed on the Abu Nidal Organisation, a Palestinian militant group.
The other two main suspects in the 1982 attack have been named as Mahmoud Khader Abed Adra, alias "Hicham Harb", who lives in Ramallah in the West Bank, and Walid Abdulrahman Abu Zayed, alias "Souhail Othman", a resident of Norway.
"Amjad Atta" is thought to have been the number three in the group's "special operations committee".
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The attack on the Chez Jo Goldenberg restaurant, a busy eaterie in the Marais district, a popular largely Jewish neighbourhood in the centre of Paris, began around midday on August 9, 1982 when a grenade was thrown into the dining room.
Two men then entered the restaurant, which had around 50 customers inside, and opened fire with "WZ-63" Polish-made machine guns.
They also shot at passers-by as they escaped down the street. The whole incident lasted only a few minutes.
At the time, France often suffered the spillover from the conflict in the Middle East, with numerous clashes involving Arabs and Jews on its soil.
Two years prior to the Goldenberg attack, a bomb exploded outside a Paris synagogue, killing four and wounding around 20.
And more than thirty years later, the French capital would again be rocked by an anti-Semitic attack, as jihadist gunmen took hostages at a Jewish supermarket and killed four -- part of the Charlie Hebdo attacks that left 17 dead in total.