The alleged incident took place on July 13th, 2003, when French and Swedish troops were deployed side-by-side as part of the European Union's Artemis military operation near the northeastern city of Bunia.
Excerpts from the documentary were broadcast last week by Swedish public service channel SVT1 and on Tuesday the French military's high command announced it had ordered a probe into the incident.
In "Joseph's Fate", made by three Swedish journalists, several Swedish soldiers criticized their superiors' passivity and the French troops' violence.
AFP was able to view the documentary before it aired on the investigative news programme Uppdrag Granskning on Wednesday evening.
The Swedish soldiers who were interviewed were never shown on screen and their identities were not disclosed.
The militia member, identified as Joseph and aged between 17 and 20, was captured outside the French-Swedish camp, the report said. French soldiers placed a noose around his neck and pushed him around with sticks, it added.
His hands were tied behind his back, his head was covered, and he was wearing only his underwear. He was interrogated for six to eight hours, during which the Swedish soldiers heard him screaming, according to the documentary.
The man was last seen by the Swedish soldiers when he was placed onboard a truck. The makers of the documentary were unable to locate him.
"We heard tormented screaming from the prisoner the whole time. It was a person who was being made to suffer, tortured," one of the Swedish soldiers said.
Electrical equipment was used during the interrogation, the documentary claimed.
The Swedish soldiers present allegedly reported the incident to their superior officers.
The case was brought to the attention of the highest ranks in the Swedish military but was kept quiet, the documentary alleged.
A spokesman for the French defence ministry, Laurent Teisseire, told AFP on Tuesday that "the Swedes conveyed this information to French authorities in the summer of 2007.
"Two military investigations have been conducted, one by the French and the other by the Swedes."
The initial French probe did not "corroborate the allegations" by the Swedish soldiers, while the Swedish investigation "turned up very contradictory results," Teisseire said.