Muhammad al-Jundi said in the complaint on Tuesday he was held by US marines for nine days and mistreated in November.
Al-Jundi was taken captive by an Iraqi group when he was working as a driver for the French journalists Christian Chesnot and Georges Malbrunot who were taken hostage in August.
Al-Jundi now lives in France. His lawyers said the civil suit was directed against General John Sattler, who was commanding the marines in Falluja at the time.
He was eventually released by being deposited on a roadside without shoes or identity papers.
Chesnot (in green jacket) hugs
al-Jundi in Paris on December 22
The lawyers said al-Jundi had little hope of success with his suit because French justice cannot investigate a complaint brought by a foreigner concerning an event that occurred abroad.
According to his lawyers, al-Jundi said US forces held him for nine days and blocked him from contacting his family. He said the marines threatened him with death.
Chesnot and Malbrunot were released in December after four months in captivity by the Islamic Army in Iraq.