Grill, who has been in the post since June 2023, won 67.22% of the votes from the 1,900 voting French rugby clubs and will remain president until autumn 2028, beyond the 2027 World Cup.
He had been up against former international Didier Codorniou.
French rugby has been rocked by a series of scandals over the recent months.
France players Oscar Jegou and Hugo Auradou were arrested in July and accused with aggravated rape after a 39-year-old woman alleged they viciously assaulted her in a hotel room hours after winning their first caps against Argentina in Mendoza.
Lawyers for the two players have asked for the case to be discontinued, with a hearing scheduled for October 25.
International full-back Melvyn Jaminet received a 34-week ban for making racist comments on social media after that same game.
And France under-18 player Medhi Narjissi was reported missing in August after going swimming in the sea in South Africa, where France were preparing for a youth tournament.
That led the FFR to pointing the finger at the "poorly managed" supervision of the team.
Looking ahead, Grill has a raft of pressing issues to tackle, notably the declining number of registered players, finances in the red and a review of France's coaching staff.
France were eliminated by eventual winners South Africa in the quarter-finals of the 2023 World Cup on French soil.
