A method for manufacturing a composite part comprising a fibrous reinforcement and a thermoplastic polymer matrix, the composite part comprising: a substrate part (110, 1110) made of a composite material comprising a continuous fibrous reinforcement in a matrix made of a first thermoplastic polymer having a first melting point comprised in a first melting temperature range; and a stiffener (120, 1120) integral with the substrate part (110, 1110), made of a fibrous-reinforced composite material in a matrix made of a second thermoplastic polymer, the stiffener comprising at least one flange (220, 1121, 1331, 1332) and at least one web (1121, 1321, 1322), the second thermoplastic polymer having a second melting point comprised in a second melting temperature range; wherein: the method being characterized in that the second melting point is higher than the first melting point; the first thermoplastic polymer is miscible with the second thermoplastic polymer at the second melting point; and in that it comprises the steps of: I) obtaining a non-consolidated preform of the substrate part; II) obtaining a preform of the stiffener comprising a layer (320, 1130) comprising the first thermoplastic polymer at a location of a flange of the stiffener configured to be in contact with the substrate part; III) placing an assembly of the non-consolidated preform of the substrate part and the preform of the stiffener contacting the substrate part in a tooling (400, 1200) comprising a molding surface reproducing a shape of the substrate part and comprising means for positioning the stiffener relative to the molding surface; and IV) subjecting the assembly to a consolidation thermomechanical cycle comprising heating under pressure up to a first temperature that is higher than the first melting temperature range but lower than the second melting temperature range in order to consolidate the preform of the substrate part and to weld the flange of the stiffener on the substrate part. a substrate part (110, 1110) made of a composite material comprising a continuous fibrous reinforcement in a matrix made of a first thermoplastic polymer having a first melting point comprised in a first melting temperature range; and a stiffener (120, 1120) integral with the substrate part (110, 1110), made of a fibrous-reinforced composite material in a matrix made of a second thermoplastic polymer, the stiffener comprising at least one flange (220, 1121, 1331, 1332) and at least one web (1121, 1321, 1322), the second thermoplastic polymer having a second melting point comprised in a second melting temperature range; wherein: the method being characterized in that the second melting point is higher than the first melting point; the first thermoplastic polymer is miscible with the second thermoplastic polymer at the second melting point; the method being characterized in that the second melting point is higher than the first melting point; the first thermoplastic polymer is miscible with the second thermoplastic polymer at the second melting point; I) obtaining a non-consolidated preform of the substrate part; II) obtaining a preform of the stiffener comprising a layer (320, 1130) comprising the first thermoplastic polymer at a location of a flange of the stiffener configured to be in contact with the substrate part; III) placing an assembly of the non-consolidated preform of the substrate part and the preform of the stiffener contacting the substrate part in a tooling (400, 1200) comprising a molding surface reproducing a shape of the substrate part and comprising means for positioning the stiffener relative to the molding surface; and IV) subjecting the assembly to a consolidation thermomechanical cycle comprising heating under pressure up to a first temperature that is higher than the first melting temperature range but lower than the second melting temperature range in order to consolidate the preform of the substrate part and to weld the flange of the stiffener on the substrate part.