A method of fabricating a composite material part including fiber reinforcement and a ceramic matrix present in the pores of the fiber reinforcement, the method including a) forming the fiber reinforcement by three-dimensionally weaving ceramic yarns, the fiber reinforcement as formed in this way presenting an interlock weave; b) forming a first ceramic matrix phase in the pores of the fiber reinforcement; c) after performing step b), introducing into the pores of the fiber reinforcement a powder that includes a mixture of SiC particles and of carbon particles; and d) infiltrating the fiber reinforcement obtained after performing step c), with an infiltration composition in the molten state including at least silicon so as to form a second ceramic matrix phase in the pores of the fiber reinforcement, thereby obtaining the composite material part.