Process for producing a composite material, characterized in that it comprises a fibrous assembly of one or more natural reinforcing fibers, impregnated with at least one amorphous or semicrystalline thermoplastic polymer and that said process comprises: i) a step of impregnation of said assembly with a precursor composition in the molten state and comprising: a) at least one prepolymer P n of said thermoplastic polymer, comprising a molecular chain P having, at its ends, n reactive functions X, with n ranging from 1 to 3, in particular n being 1 or 2, preferably 2, said prepolymer P n having a number-average molecular weight Mn ranging from 500 to 10 000, preferably from 1000 to 10 000, more preferentially from 1000 to 6000 and even more preferentially from 1000 to 2500 g.mol -1, as determined by potentiometry, b) at least one chain extender Y-A-Y comprising functions Y which react with at least one of said functions X, ii) a step of bulk polymerization by poly(addition), in the molten state, of said prepolymer with said chain extender, and in which: - said thermoplastic polymer of the thermoplastic matrix is the result of said bulk polymerization by polyaddition of said precursor composition and - said impregnation i) and polymerization ii) steps take place at a temperature below 250°C, in particular below 245°C, preferably below 230°C, particularly preferably below 210°C, more preferentially below 200°C and even more preferentially not exceeding 190°C. i) a step of impregnation of said assembly with a precursor composition in the molten state and comprising: a) at least one prepolymer P n of said thermoplastic polymer, comprising a molecular chain P having, at its ends, n reactive functions X, with n ranging from 1 to 3, in particular n being 1 or 2, preferably 2, said prepolymer P n having a number-average molecular weight Mn ranging from 500 to 10 000, preferably from 1000 to 10 000, more preferentially from 1000 to 6000 and even more preferentially from 1000 to 2500 g.mol -1, as determined by potentiometry, b) at least one chain extender Y-A-Y comprising functions Y which react with at least one of said functions X, a) at least one prepolymer P n of said thermoplastic polymer, comprising a molecular chain P having, at its ends, n reactive functions X, with n ranging from 1 to 3, in particular n being 1 or 2, preferably 2, said prepolymer P n having a number-average molecular weight Mn ranging from 500 to 10 000, preferably from 1000 to 10 000, more preferentially from 1000 to 6000 and even more preferentially from 1000 to 2500 g.mol -1, as determined by potentiometry, b) at least one chain extender Y-A-Y comprising functions Y which react with at least one of said functions X, ii) a step of bulk polymerization by poly(addition), in the molten state, of said prepolymer with said chain extender, and in which: - said thermoplastic polymer of the thermoplastic matrix is the result of said bulk polymerization by polyaddition of said precursor composition and - said impregnation i) and polymerization ii) steps take place at a temperature below 250°C, in particular below 245°C, preferably below 230°C, particularly preferably below 210°C, more preferentially below 200°C and even more preferentially not exceeding 190°C. - said thermoplastic polymer of the thermoplastic matrix is the result of said bulk polymerization by polyaddition of said precursor composition and - said impregnation i) and polymerization ii) steps take place at a temperature below 250°C, in particular below 245°C, preferably below 230°C, particularly preferably below 210°C, more preferentially below 200°C and even more preferentially not exceeding 190°C.