The invention relates to a method of fabricating a composite material part comprising fiber reinforcement densified by a matrix, the method comprising the steps of: making a fiber preform consolidated by impregnating (S4) a fiber texture made up of yarns with a liquid consolidation composition containing a precursor for a consolidating material, and by transforming (S7) the precursor into consolidating material by pyrolysis so as to obtain a consolidated preform that is held in shape; and densifying (S8) the consolidated fiber preform by chemical vapor infiltration; the method being characterized in that it includes, prior to impregnation (S4) of the fiber texture with the consolidation liquid composition, a step of filling (S2) the pores of the yarns of said fiber texture by means of a filler composition.