French authorities suspect Hassan Diab, 59, was involved in the anti-Semitic bombing of a Paris synagogue in 1980 that killed four people and injured dozens of others.
Diab denies any role in the deadly attack, saying the unwavering moral principle throughout his life has been to promote equality and respect for all.
Lawyers for Diab are challenging the decision to extradite him in the Court of Appeal for Ontario, arguing before the panel of three judges that fundamental mistakes were made.
His lawyers say the case centres on a handwriting analysis that linked Diab to the bombing, which they say is unreliable as three defence experts have challenged it.
But the Crown says there are different standards for evidence at trials and for extraditions, and the handwriting analysis isn't unreliable simply because it's three against one.
Diab was committed for extradition in 2011 to face French authorities, even though Ontario Superior Court Judge Robert Maranger acknowledged the case against him was weak.
He had to surrender himself into custody for the duration of the appeal hearing.
In April last year, then-justice minister Rob Nicholson signed an extradition order surrendering Diab to France.
The RCMP arrested Diab, a Canadian of Lebanese descent, in November 2008 in response to a request by France.
Diab's lawyers are arguing that Nicholson made several mistakes, including opting to surrender him even though France has not yet decided whether to put him on trial for the bombing.