Three different fan clubs have filed the lawsuit using French defamation laws that make it an offence to sully the image of a dead person. US or British laws do not provide this protection.
The Michael Jackson Community, the MJ Street and On the Line groups are seeking symbolic damages of €1 each.
Emmanuel Ludot, the fans' lawyer, likened the men's allegations to a "genuine lynching" of Jackson.
"In France you cannot sully the image of the dead," Mr Ludot said. "There's moral and emotional suffering. And when there's suffering, there's compensation. It's very simple."
In 2014, he represented the Michael Jackson Community when the group successfully won nominal damages of €1 from the pop star's private doctor, Conrad Murray, for his part in Jackson's death in 2009 aged 50.
Mr Robson and Mr Safechuck were not in court and did not instruct lawyers to represent them.
In Leaving Neverland, the two men said they were befriended by Jackson and abused by him from the ages of seven and 10 in the early 1990s.
Jackson was acquitted in 2005 on charges of molesting a different boy, and his family has denied the accusations made in the documentary.
The film, which was released in January, broke streaming records and prompted the Jackson family to sue for $100m.
After it was broadcast in France, some radio stations stopped playing his music and Louis Vuitton removed Jackson-themed items from its 2019 summer menswear collection.
The creators of The Simpsons also decided to pull a 1991 episode from future broadcasts because it featured Jackson's voice.
Additional reporting by Reuters