The Paris public prosecutors' office has concluded there is "sufficient evidence" against Hassan Diab to justify a trial, allowing the court to decide on the doubts as to his whereabouts at the time of the attack, a source told the AFP news agency on Wednesday.
An investigating magistrate will make the final decision on whether the case will go to trial on chrages of murder, attempted murder and destruction of property as part of a criminal conspiracy.
The bombing of the synagogue in Paris's rue Copernic on 3 October 1980 when it was packed for Sabbath prayers killed four people and injured about 40.
Diab, a 64-year-old sociology teacher at a university in Ottawa, is accused of having carried out the attack on behalf of a breakway group from the Popular Front for the Liberation of Palestine (PFLP).
Prosecutors believe he planted the bomb in the saddle-bag of a motorbike parked outside the synagogue.
The evidence against Diab includes testimonies that he was a member of the PFLP Special Operations group, a sketch of the bomber that resembles him, handwriting analysis and a passport in his name with entry and exit stamps for Spain that would place him in Europe at the time of the bombing.
But the claims of PFLP-SO membership have been challenged, other experts disagree with the handwriting analysis and Diab claims to have been taking exams in Beirut at the time, a claim that is backed by his ex-wife, Nawal Copty.
Canadian police arrested Diab on a French request in 2008 and he was extradited six years later.
With the prosecutor admitting to "seriously doubting" that he planned the bomb, Diab has twice been granted bail in France but both times the decision has been overturned on appeal.
A group of Canadian artists, activists and politicians, including filmmakers Atom Egoyan and political activist Naomi Klein, have taken up his case, urging Canadian Prime Minister Justin Trudeau to intervene to secure his release.