A process for manufacturing a component with an insert made of a composite is disclosed. The composite includes a metal matrix, within which ceramic fibers extend. The insert is made of a composite which is obtained from a plurality of coated filaments, each filament includes a ceramic fiber coated with a metal sheath. The process includes winding a bundle or bonded sheet of coated filaments around a body of revolution perpendicular to the axis of rotation of said body. The insert is then subjected to a hot isostatic pressing step in a container. The process is applied to the manufacture of aeronautical turbomachine components.