Vous pouvez trouver l’explication ici :

Le nom d’Ulysse existe sous plusieurs formes en grec ancien ; on
trouve par exemple : Ὀλυσσεύς / Olusseús, Ὀλυττεύς / Olutteús,
Οὑδυσσεύς / Houdusseús ; Οὐλιξεύς / Oulixeús et Οὐλίξης / Oulíxês.
L’emprunt latin Ulixēs vient de cette dernière forme. Le nom d’Ulysse
donne naissance à quelques dérivés : Ὀδυσσεία / Odusseía (l’Odyssée),
Ὀδὐσσειον / Odússeion (sanctuaire d’Ulysse) et Ὀλισσεῖδαι /
Olisseîdai, nom d’une phratrie à Thèbes et Argos.

I got curious and searched about.

Odysseus is the greek name of the hero, and Ulysses is the name how the Romans known him.

The first reference, in english, that I found.

Since the French language descended from the Latin of the Roman Empire, it makes sense.

I think that @Dimitris’s answer can point in the right direction (i.e. in Greek the character of Odysseus was known under various names including Oulixeus/Οὐλιξεύς from which the Latin name was derived), nevertheless I would like to add something to it in order to take into account the historical context of the translation of Homer’s works into French.

The first translation of The Iliad¹ in Middle French was made by Jean Samxon and published between 1519 & 1530. This version was based solely on the Latin translation, so it is easy to understand he worked from the Latin name of Ulixes/Ulysses.
A second translation was made by Hugues Salel and published in 1545. It is not known for a fact whether Hugues Salel had access to the Greek text² but at least one scholar thinks he worked with both, the Greek text and a Latin text (by L. Valla)³.

Jacques Peletier du Mans’s translation of The Odyssey was published in 1547. Peletier du Mans was a member of the Pléiade and we can imagine he was well versed in Greek as well as in Latin.

So back to your question: I speculate that the Renaissance elite (those who would read The Iliad and The Odyssey) had already become acquainted with the name Ulysse through Samxon’s and Salel’s texts and therefore, even if he could read Greek, Peletier du Mans thought better to continue with Ulysse.

^{1 In which the character of Ulysse fisrt appears.
2 Source : http://expositions.bnf.fr/homere/grand/069.htm
3 See Didier Pralon, a professor in Ancient Greek language and literature. We can read this scholarly paper on the French translations of The Iliad.}