The appeal to the Court of Cassation is not a third level of jurisdiction. The Court does not re-examine the facts; it checks that the lower courts applied the law correctly. If it quashes, it remands the case to another court of appeal.
Non-admission is a filter. Introduced to relieve the Court's backlog, it allows a panel of three judges to dismiss, after the briefs have been filed, an appeal that is inadmissible or lacks any serious ground — without detailed reasoning.
The wording matters. Writing that “the Court of Cassation upheld the judgment” is inaccurate: it upheld nothing. It considered that no ground justified examination. The appeal judgment simply becomes irrevocable.
That is what happened on 10 May 2002 in the Collorafi case: the appeal was declared non-admitted, which made the judgment of the Paris Court of Appeal of 8 March 2000 final.