A method of fabricating a composite material part having carbon fiber reinforcement densified by a matrix, including making a coherent fiber preform of carbon fibers presenting holes formed from at least a first face of the preform, and densifying the preform by depositing therein a material constituting a matrix by means of a chemical vapor infiltration type process. The holes are formed by causing a plurality of non-rotary elongate tools to penetrate simultaneously, the tools being substantially mutually parallel and presenting on their surfaces roughnesses or portions in relief suitable for breaking and/or transferring fibers they encounter, the tools being caused to penetrate simultaneously by moving a support carrying the tools, and the tools being selected to have a cross-section that makes it possible to obtain in the carbon fiber preform holes that present a cross-section with a mean dimension lying in the range 50 μm to 500 μm.