In its ruling, the appeal court said both the lower-court judge, and subsequently the federal justice minister, made no legal errors in coming to the conclusion Hassan Diab should be handed to French authorities.
Diab and several supporters will be holding a news conference on Parliament Hill at noon to discuss the ruling.
French authorities allege Diab, 60, was a member of the Popular Front for the Liberation of Palestine, which made and planted a bomb that killed four people and injured more than 40 on Oct. 3, 1980, outside the Copernic Street synagogue in Paris.
But Diab has denied any role in the attack and insists his case is one of mistaken identity.
The RCMP arrested Diab — a Canadian of Lebanese descent who has taught sociology at Carleton University and the University of Ottawa — in Gatineau, Que., in November 2008 in response to a request by France.
In June 2011, Ontario Superior Court Justice Robert Maranger committed Diab for extradition to face French authorities despite acknowledging the case against him was weak.
The following April, then-justice minister Rob Nicholson signed an extradition order surrendering Diab to France.