A process for manufacturing a composite part includes introducing an adhesion promoter into the pores of a fibrous preform formed by threads covered with a coating having —OH groups on its surface, the adhesion promoter including an electron-withdrawing group G1 that is reactive according to a reaction of substitution or of nucleophilic addition with the —OH groups, and a reactive group G2; grafting the adhesion promoter to the surface of the coating by a reaction of substitution or nucleophilic addition of the —OH groups on the group G1; introducing a ceramic precursor resin into the pores of the fibrous preform; polymerizing the resin introduced and bonding the grafted adhesion promoter to the resin by chemical reaction between these two compounds at the level of the group G2, and forming a ceramic matrix phase in the pores of the fibrous preform by pyrolysis of the polymerized resin.