The FFR alleged Noves was guilty of serious misconduct, but a Toulouse labour tribunal decided otherwise. Noves was asking for 2.88 million euros.
Both parties have the right to appeal, although initial reactions suggested that they had accepted the outcome.
"I am satisfied with this decision. The FFR said there was serious misconduct and the tribunal said there was none," Noves, the first France rugby union coach to be sacked, told reporters.
"I don't know if we are going to appeal, we have a month to do so. The demands (from Noves) were excessive and the decision is reasonable," the FFR's lawyer Joseph Aguera told French sports newspaper L'Equipe.
The FFR later welcomed a "balanced" decision and said in a statement it did not plan to appeal.
Noves was sacked by the FFR in December 2017 after winning seven of his 21 matches in charge, while his contract was due to run until the end of this year's World Cup in Japan.
Noves, 65, was replaced by Jacques Brunel, who has been struggling to turn the situation around.
France beat Scotland and Italy in this year's Six Nations but lost against England, Ireland and Wales to finish fourth.
(Reporting by Julie Rimbert, writing by Julien Pretot; Editing by Christian Radnedge and Ken Ferris)
