Ubaid al-Braiki, a member of the executive bureau for Tunisia's general labour union, said the union would look into Hached's request.
The documentary film included testimony from a member of a secret French organisation known as The Red Hand (La Main Rouge) who said he was responsible in part for Hached's assassination.
"I believe what I did was legitimate, and I would do it again if I had to," Antoine Melero said.
"Hached's assassination was definitely committed by La Main Rouge in agreement with French government officials in Tunisia.
"The group that has committed the assassination was never prosecuted in Tunisia, it was sent back to France as agreed with the Tunisian authorities."
There was no immediate comment on the allegations from French officials.
Melero also implicated Habib Bourguiba, the late Tunisian president, in the killing.
"Bourguiba played a key role as he knew about Hached's assassination," Melero said in the film.
"He was content with Hached's assassination as was France" because it wanted to hand over the rule to Bourguiba," he said.
"I believe that Tunisia's independence was expected long time before then, and France knew that. It wanted to hand over the power to one of its friends, and that is why it chose Bourguiba."
Farhat Hached was viewed by many Tunisians as a symbol of the country's struggle against the French colonisation.
He was killed on December 5 on the outskirts of the city of Tunis when armed attackers opened fire on his car.