Dieudonné has five days to remove the passages from the web or face a fine of 500 euros per section for every day they stay online.
France's Union of Jewish students (UEJF), which brought the legal action, said it would also approach YouTube to ensure "they respect their legal obligations in the future".
YouTube did not comment on the video in question but restated its position: "We don't pull a video unless it breaches our community rules or if it is ruled by a court. "
In one passage, Dieudonné claims "I was born in '66, so wasn't born [...] know nothing about the gas chambers" but says he can organise a meeting with "Robert", a reference to negationist former academic Robert Faurisson.
This section was part of his banned show Le Mur.
Opponents led by French government succeeded in preventing Dieudonné from touring his latest show but not succeed in making him any less popular.
Dieudonné's finances have also been targeted as he has not paid any of the fines for previous race-hate convictions and is suspected of money-laundering his assets.