The lawmakers insist the Taliban and al-Qaida suspects should face French justice, denouncing the legal limbo that has allowed some detainees to be held for two years without charge.
One Communist lawmaker, Andre Gerin, said deputies from both the centre-right ruling party and the left-wing opposition had all signed, expressing their wish to see the six face "judgement from the tribunals of our own country".
The United States has been holding more than 600 detainees of various nationalities in the Guantanamo base for nearly two years, claiming they are "illegal combatants".
Under this classification, the prisoners are not charged, but nor are they allowed access to any legal process.
Various human rights groups, as well as national governments have denounced the lack of due process provided to the suspects, some of whom have been returned to their home countries.
One lawyer who visited his client also believes the 600 are not being treated equally. Stephen Kenny was the first civilian lawyer allowed access to any of the former Afghan war suspects being held at the military facility.
"The standard of justice seems to have different layers, one for the Americans ... a different one for ... the rest of them in the camp"
lawyer for Australian captive
He told the BBC's World Today programme on Thursday there was a pecking order of treatment depending on the captive's nationality - with Americans on top.
"I see a great destruction of what I would call the rule of law, that people should be treated equally before the law, that they should have the same standard of justice," he said.
But in order to be allowed to see his client, Kenny had to sign a legal document preventing him from talking about anything related to Guantanamo Bay and what he saw there without the permission of the US military authorities.
Nevertheless, the lawyer who now represents Australian detainee David Hicks said inmates appeared to be treated differently depending on whether they came from countries that had allied themselves with the Americans or not.
"This is a case where the standard of justice seems to have different layers, one for the Americans, there may be another one for the British, there is certainly a different one for Australian - less than the American.
"The rest of them in the camp... they weren't [part of] the allies' camp is their rationale and they will get a lesser standard than what the Australians will."