The six-season deal runs from 2018-19 to 2023-24 and covers all of France's national teams. Le Coq Sportif will replace German sportswear giant adidas in the role.
The FFR said that it received three offers from prospective kit suppliers, but did not disclose details. Earlier this week RMC Sport reported that US manufacturer Under Armour had expressed an interest.
The first international tournament of the new deal will be the Rugby Sevens World Cup, which takes place in the US city of San Francisco from July 20-22, 2018.
The FFR said that Le Coq Sportif would provide €1.9m ($2.1m) per season to amateur rugby teams as part of the agreement.