Judge Sophie Clement wants permission from the US authorities to inspect and copy all documents relating to the three men and to interview all persons who had contact with them there, according to legal documents seen by AFP.
The judge requested access to "all documents relating to the justification and modalities of (US) armed operations in Afghanistan and Pakistan and to the treatment of persons arrested during these operations," the documents said.
They were allowed to return to France in 2004 and 2005 and were detained for periods of between 11 and 17 months.
They were sentenced by a French court to one year in prison on terrorism charges in 2011 but have said they will appeal that decision.
A lawyer representing two of the men, William Bourdon, said Judge Clement's request to US authorities was "without precedent and should enable us to identify those responsible for this arbitrary detention and torture."
Benchellali said that soon after his arrest he was taken to Kandahar in Afghanistan where he says he was beaten and forced to strip, and then made to lie on top of other naked men while US soldiers took photos.
Ben Mustapha said he was subjected to sexual abuse in Kandahar, which judge Clement said in the legal documents might lead to rape charges.
All three former inmates told of gruelling interrogations during which they were beaten. They also said that they were put in cells and subjected to blasting music from several sources to deprive them of sleep.
Ben Mustapha said interrogators would provoke inmates by trampling on the Koran or throwing the Muslim holy book into buckets of prisoners' excrement.
The US base at Guantanamo, Cuba, accepted its first prisoners from the battlefields of the US-led "war on terror" on January 11, 2002, four months after al-Qaeda flew hijacked jets into the World Trade Center and the Pentagon.
Obama declared within a few hours of taking office in January 2009 that he would shutter the camp within a year, saying it was used as a recruiting tool for terrorists, and detrimental to US national security.
But in the face of deep opposition in Congress to moving inmates to the US mainland or holding civil trials for key al-Qaeda suspects, Obama has failed to live up to his vow.
A decade on, 171 prisoners remain there, most in legal limbo, some awaiting transfer abroad, and at least 40 may never face justice but are deemed too dangerous to ever be freed.
A dozen European countries from Ireland to Albania have accepted more than 50 former inmates who are either citizens, former residents or, in many cases, cannot be returned to their home countries for fear of ill-treatment.