The complaint was filed with the prosecutor's office specializing in crimes against humanity at the Paris judicial court, said their lawyer, Jessica Finelle.
In a press release, Finelle said that the victims' families, "expect a lot from French courts."
Since October 2019, hundreds of thousands of Iraqis have demonstrated to denounce the corruption of power. Called the "October Revolution", this unprecedented revolt also demanded services and jobs for all.
Nearly 600 people have been killed, and 30,000 others have been injured, since October 1, 2019. The assassinations and kidnappings of activists continue in Baghdad and southern Iraq.
In her 80-page complaint, Finelle documented, "the involvement of the authorities in general and Prime Minister Abdel Mahdi in particular" in these crimes.
"The former Prime Minister did not take any measures to prevent these crimes. He deliberately favored the installation of a climate of impunity encouraging their renewal", Finelle added.
This complaint filed in Paris under France's universal jurisdiction in matters of torture and enforced disappearances is also based on the fact that Abdel Mahdi lived in France for about thirty years.