During the French team's tour of Argentina earlier this month, the Toulon player was filmed saying: "The first Arab I come across, I’ll throw him a headbutt."
The FFR's Disciplinary Council ruled that Jaminet had “undermined the best interests of rugby.”
Eight of the 34 weeks can be replaced by a series of actions by the player, including alcohol and social media awareness and speaking at rugby schools "to promote the values of sport relating to the fight against discrimination."
Jaminet has previously apologised for his comments, saying: "I understand that this may have hurt and offended many people, and I want to make it clear that these comments in no way reflect my values or those of the French rugby team.
"Racism, in all its forms, is unacceptable and goes against everything I believe in."
A day after the incident, two other touring French players, Oscar Jegou and Hugo Auradou were arrested after an allegation of sexual assault.