The court in Versailles heard an Argentine government appeal against a lower court's refusal to extradite Mario Arturo Sandoval, who is accused of committing about 100 crimes against humanity between 1976 and 1979.
The French state's advoacate general did not oppose extradition in Thursday's hearing, while Sandoval's lawyer claimed this was a case of mistaken identity.
The court said it would deliver its ruling on 19 October.
Sandoval, 64, has lived in France since 1985 and has had French nationality for about 20 years.
Argentine judge Sergio Torres launched the extradition appeal in 2012 as part of his inquiry into abuses committed at a naval college that was used as a secret detention centre under military rule.
In May 2014 a Paris court agreed to extradite Sandoval but that decision was overturned on appeal in February 2015.
French courts are considering one case, that of architecture student and political activist Hernan Abriata, who disappeared in 1976 at the age of 26, eight months after his marriage.
Thousands disappeared under military rule
According to official accounts, almost 20,000 people disappeared after being kidnapped by the military under the dictatorships, although rights groups put the figure at 30,000.
Some of them were thrown alive into the sea from aircraft, while others' bodies were dumped in rivers or buried in secret.
In some cases their children were adopted by their murderers or other military families, only to discover who their real parents were when they were adults.
Torres's inquiry was only possible after the repeal of an amnesty for crimes committed under military rule in 2003.
He identified more than 1,000 victims at the college but was only able to find the bodies of 547.
Abriata's body has never been found and Sandoval is accused of being the leader of the death squad that seized him at his home in October 1976.
The former police officer, who became an economic intelligence expert and part-time lecture at the Sorbonne's Latin America department after coming to France, denies the allegations, claiming at one point that the guilty man was someone who had the same name as him, at another that he was the victim of political persecution.
Although enforced disappearance is recognised as a crime in Argentina and in a UN convention signed by France, it does not figure in the French penal code.
Bizarrely, if Abriata can be considered to be dead, the crime would be covered by the statute of limitations and the extradition appeal would be turned down, while if his death cannot be declared in the absence of a body the crime can be considered to be ongoing and extradition could go ahead.
The Argentine government's lawyers point out that French courts have already punished Latin Americans for their role in similar crimes, notably 13 Chileans found responsible in 2010 for the disappearance of French citizens under the Pinochet dictatorship of the 1970s.
They also point out that the crime is recognised by international jurisprudence thanks to the UN convention, which France was involved in draughting.
But such cases remain sensitive in France, according to experts, because of concerns that French citizens could be prosecuted for alleged crimes against humanity committed during colonial wars.
Abriata's family has appealed to President Emmanuel Macron to intervene to ensure that Sandoval faces a court in Argentina.