A process for a composite material, including an assembly of one or more reinforcing fibers, impregnated with at least one thermoplastic polymer with a glass transition temperature Tg of less than or equal to 75° C. and a melting point of from 150° C. to less than 250° C. or a Tg of greater than 75° C., the process including: i) a step of impregnating said assembly in bulk melt form with at least one thermoplastic polymer, which is the product of polymerization by polyaddition reaction of a reactive precursor composition including: a) at least one prepolymer P(X)n of said thermoplastic polymer, and b) at least one chain extender, represented by Y-A-Y, ii) a step of cooling and obtaining a fibrous preimpregnate, and iii) a step of processing and final forming of said composite material.