The method comprises: using chemical vapor infiltration to form a first continuous interphase on the fibers of a fiber structure made of refractory fibers, the interphase having a thickness of no more than 100 nanometers; impregnating the fiber structure with a consolidation composition comprising a carbon or ceramic precursor resin; forming a fiber preform that is consolidated by shaping the impregnated fiber structure and using pyrolysis to transform the resin into a discontinuous solid residue of carbon or ceramic; using chemical vapor infiltration to form a second continuous interphase layer; and densifying the preform with a refractory matrix. This preserves the capacity of the fiber structure to deform so as to enable a fiber preform to be obtained that is of complex shape, while nevertheless guaranteeing the presence of a continuous interphase between the fibers and the matrix.