The invention relates to a process for improving the adhesion of carbon fibers by coating a surface of the carbon fibers with a polymer film containing functional groups capable of acting as chain transfer agents during a chain transfer polymerization of a resin curable by chain transfer polymerization to obtain coated carbon fibers. The coated carbon fibers are then contacted with the curable resin, and the chain transfer polymerization of the curable resin is induced to produce an organic matrix and forming a composite material. The functional groups of the polymer film act as chain transfer agents during the chain transfer polymerization of the curable resin and thereby improve adhesion of the carbon fibers to the organic matrix. Applications of this invention include aeronautical, aerospatial, shipbuilding, railway and motor vehicle industries, armaments industry, sports and leisure articles, and the like.