According to this doctrine, foreigners can be prosecuted for crimes committed anywhere in the world.
Ely Ould Dah, 42, was not in the court on Thursday in the southern town of Nimes, having fled France in 2000 several months after being charged with torture and crimes against humanity.
"This trial takes place thanks to the doggedness of the victims as well as the FIDH," the organisation's president Sidiki Kaba said.
Ould Dah, who is today a major in the Mauritanian army, is alleged to have tortured two officers in 1991 after they were accused of taking part in a plot against President Maaouiya Ould Taya.
In July 1999 he was detained in France while on a training course in the city of Montpellier.
He was granted conditional release in September and fled back to Mauritania in unclear circumstances the next April.
Court proceedings began with evidence from Mamadou Youssef Daigana, a 45-year-old former Mauritanian army lieutenant who is one of five civil plaintiffs in the case.
Arrested and tortured
Daigana described being arrested in a round-up and subjected to different types of torture.
"One method was to bury the prisoner up to his neck in sand and beat him till he passed out. In the Jaguar method, we were suspended from a bar and hit with lengths of cable and sticks," he said.
"One method was to bury the prisoner up to his neck in sand and beat him till he passed out. In the Jaguar method we were suspended from a bar and hit with lengths of cable and sticks"
Mamadou Youssef Daigana, former Mauritanian army lieutenant (plaintiff)
The doctrine of "universal jurisdiction" has been making inroads into international law ever since the detention of former Chilean president Augusto Pinochet in London in 1998.
Several cases have been launched in European courts - including one citing Israeli Prime Minister Ariel Sharon in Belgium - but in practice it is proving difficult to bring them to trial.