Miller, who is now retired from the military and working as a consultant, was in charge of Guantanamo from 2002 to 2004 before being put in charge of detention in Iraq, a role that included oversight of the notorious Abu Ghraib facility.
Former Guantanamo detainees Nizar Sassi and Mourad Benchellali have filed cases against him, citing their own experiences in the prison and evidence of alleged torture collected by rights campaigners.
Both were arrested in Pakistan and flown to Guantanamo, suspected of links to Al Qaeda.
But, as with other Guantanamo detainees, they were never charged and then-president George Bush's adminstration argued that they were not covered by the Geneva Convention on treatment of prisoners of war, designating them "enemy combatants" and authorising "enhanced interrogation techniques".
Those techniques included prolonged sensory deprivation, exposure to extreme temperatures, stress positions, the use of dogs, subjection to loud music and flashing lights, humiliation, face and body slaps and waterboarding.
In previous submissions to the French court in this case, the US-based Center for Constitutional Rights (CCR) details the use of these techniques and the legal debate within the adminstration as to whether they constitute torture.
The CCR accuses Miller of personal responsibility in authorising their use and says he listed nine techniques that had been rescinded by Secretary of State Donald Rumsfeld as "essential to mission success".
It also says that he advocated their use in Iraq on a visit there before his transfer, although abuses of prisoners in Abu Ghraib had already come to light.
The US failed to reply to requests from Judge Sophie Clément to visit Guantanamo Bay and have access to relevant documents and people who had contact with the plaintiffs.
Clément agreed to subpoena Miller last month, although the plaintiffs' lawyer, William Bourdon, admitted that it was unlikely he would turn up.
US President Barack Obama has proposed the closure of Guantanamo Bay on several occasions, most recently on 23 February, but been blocked by the Republican-dominated Congress.
He has refused to take legal action against officials overseeing the facility and blocked lawsuits by alleged victims on the grounds of state secrecy.
Bourdon told the Intercept website that he would apply for an arrest warrant but that it would only be enforceabe if he comes to France.
Similar cases are under way in Spain and Germany.