The French billionaire - who married the Mexican beauty in 2009 - is confirmed in court papers in New York as being the father of the four-year-old boy, as well as being the dad of his and Salma's daughter Valentina, also four.
Linda was seen in court yesterday (30.06.11) trying to reach an arrangement regarding support for the young boy, but no such agreement has been reached.
Francois was not there to witness the legal proceedings, something his lawyer David Aronson claims is a misunderstanding.
He told the New York Post newspaper: "We had understood that it was to be a brief telephone conference, to bring Magistrate Troy up to date on what the status was."
It is believed to be the third or fourth time Linda has visited court, meaning it is likely to go to a full support trial.
Salma, 44, recently revealed she thought of herself as a "good housewife" as she regularly concocted home-cooked meals for her husband.
She said: " I am a housewife. I cook every night for my husband. I am most definitely a housewife. And a good one, I must say.
"Our life is great and glamorous in many ways, and in many ways - the good ways - it's very homey. He's a spoilt brat, my husband, when it comes to food."