A process for manufacturing a one-piece axisymmetric part includes: superposition, around a rotating cylindrical mandrel of at least respectively inner and outer metal-coated composite fibrous structures, wound in first and second crossed directions on the mandrel; arranging, between the crossed inner and outer fibrous structures, at least one layer of metallic wire; then placing a blank of the part, formed by the fibrous structures and the layer of metallic wire, in a tool to apply to the blank a hot isostatic pressing treatment, and to obtain the part.