Criminal Code of the French Republic (as of 2022) 
(unofficial translation) (emphasis added)
Excerpts related to Hate crime offences

Articles 132-76 and 132-77 on aggravating circumstances provide that the maximum of the custodial sentence incurred is increased when a crime or offense is preceded, accompanied or followed by words, writings, images, objects or acts of any kind that either offend against the honour or consideration of the victim or the group of persons of which the victim is a member on “the grounds of his or her membership or non-membership, actual or supposed, of a particular race, ethnic group, nation or religion”, “his or her sex, sexual orientation or actual or supposed gender identity, or establish that the acts were committed against the victim for one of these reasons”.
On 29 April 2024, a circular relating to the judicial treatment of offences committed on the grounds of membership or non-membership of a religion, in a separatist context or where the principle of secularism is under attack, was distributed in order to invite prosecutors to mobilise, in particular, the aggravating circumstance attached to the victim’s membership or non-membership, actual or supposed, of a particular religion.

Excerpts related to Hate speech offences

Press Freedom Act of the French Republic of 29 July 1881 (as of 2021) (excerpts)
Article 24 imposes criminal penalties on "those who, by any of the means set out in Article 23*, incite discrimination, hatred or violence against a person or group of persons on the grounds of their origin or their membership or non-membership of a particular ethnic group, nation, race or religion”, “their sex, their sexual orientation or gender identity or their disability".
*Article 23: speeches, shouts or threats expressed in public places or meetings, or by writings, printed matter, drawings, engravings, paintings, emblems, images or any other written, spoken or pictorial material, sold or distributed, offered for sale or displayed in public places or meetings, either by posters or notices displayed for public view, or by any means of electronic communication”. 
The purpose of the incitement must be to induce those to whom it is addressed to behave in a discriminatory, hateful or violent way.