A porous fiber structure is consolidated by forming within a deposit of a refractory material by partially densifying the fiber structure in such a manner as to bond together the fibers of the fiber structure so as to enable the fiber structure to be handled without being deformed, while leaving empty the major fraction of the initial pore volume of the fiber structure, and rigid pins are implanted through the consolidated porous structure. A blank is obtained by reinforcing a fiber structure by implanting pins or by bonding together consolidated fiber structures, the bonding being performed by implanting pins. A composite material part is obtained by densifying the blank.