Foreign Minister Jean-Noel Barrot posted on X that the arrest had been made possible by President Emmanuel Macron's decision to recognise an independent Palestinian state on Monday, "enabling us to request extradition".
Macron welcomed the co-operation with the Palestinian Authority, adding: "We are working together towards a swift extradition".
At the time, the grenade and gun attack on the Jo Goldenberg restaurant in the heart of the Jewish district of the Marais quarter in August 1982 was the deadliest anti-Semitic attack in France since World War II.
It was part of a wave of overseas violence by Palestinian militants that had begun in the 1970s.
No one has yet been tried in connection with the case.
Along with France, about 10 countries including Australia, Belgium, the United Kingdom and Canada are expected to formally recognise a Palestinian state on Monday, before the annual leaders' gathering at the United Nations General Assembly.
Barrot said that "nothing can alter France's determination to take action against terrorism and anti-Semitism".
The National Anti-Terrorism Prosecutor's Office (PNAT) said in a statement that Interpol had informed it of the arrest of Mahmoud Khader Abed Adra, alias Hicham Harb, by Palestinian authorities.
In July, French judges ordered the trial of six people including Harb in a special terrorism court over the attack.
