The migrants - 37 Sudanese and one Eritrean - claim they were victims of "acts of torture and degrading treatment" on arrival on the Italian islands of Lampedusa and Sicily.
Most of them crossed the Mediterranean from Libya.
They claim to have suffered mistreatment after refusing to have their fingerprints taken, as required by the EU's "Dublin rules", which stipulate that a migrants' asylum applications must be dealt with in the country where they arrive.
They were "mistreated, some beaten, very often arbitrarily detained, blackmailed, and deprived of food and water", according to their lawyer, Isabelle Casau.
Two claim to have been tortured, "one having his armed broken the other his testicles crushed", she said.
Their fingerprints were eventually taken and they were sent to camps, from which they escaped to go to France, where they arrived in the middle of last year.
They wish to stay here, according to Casau, but the authorities are preparing to send them back to Italy.
Although the alleged abuses took place in Italy, the court in Pau is able to hear the case because of the seriousness of the charges, the lawyer told the AFP news agency.
As well as French law, the legal complaint cites European human rights legislation and the UN's convention against torture.