A method for producing a part, comprising at least one reinforcing element manufactured from a fibrous insert made from a composite material, using an injection mold comprising a first part and a second part, each comprising a molding surface (22a, 22b), said molding surfaces (22a, 22b) defining a molding cavity between them having the form of the part to be produced, the method comprising the following steps: - transporting and positioning the fibrous insert on the first part of the injection mold by at least one gripping element of a gripping device, the gripping device further comprising a shaping wall, the gripping element being able to be actuated between an inactive configuration, in which it does not interact with the fibrous insert, and an active configuration, in which it is able to keep the fibrous insert on the gripping device, the gripping element being in the active configuration during the transport and positioning; - shaping the fibrous insert into the reinforcing element against the molding surface of the first part; - injecting a plastic material in the injection mold, such that the reinforcing part is overmolded by the plastic material and the part is produced; the method being characterized in that it comprises the following steps: during the positioning of the fibrous insert on the molding surface of the first part: bringing the fibrous insert closer to the molding surface of the first part while maintaining a separation between said molding surface and the fibrous insert; and moving the shaping wall relative to the gripping element so as to apply the fibrous insert against part of the molding surface; and during the shaping of the fibrous insert: applying the shaping wall and the gripping element against the fibrous insert and the molding surface of the first part, such that the fibrous insert acquires the shape of the molding surface, the gripping element being actuated from its active configuration to its inactive configuration before said application of the shaping wall. - transporting and positioning the fibrous insert on the first part of the injection mold by at least one gripping element of a gripping device, the gripping device further comprising a shaping wall, the gripping element being able to be actuated between an inactive configuration, in which it does not interact with the fibrous insert, and an active configuration, in which it is able to keep the fibrous insert on the gripping device, the gripping element being in the active configuration during the transport and positioning; - shaping the fibrous insert into the reinforcing element against the molding surface of the first part; - injecting a plastic material in the injection mold, such that the reinforcing part is overmolded by the plastic material and the part is produced; the method being characterized in that it comprises the following steps: during the positioning of the fibrous insert on the molding surface of the first part: bringing the fibrous insert closer to the molding surface of the first part while maintaining a separation between said molding surface and the fibrous insert; and moving the shaping wall relative to the gripping element so as to apply the fibrous insert against part of the molding surface; and during the shaping of the fibrous insert: applying the shaping wall and the gripping element against the fibrous insert and the molding surface of the first part, such that the fibrous insert acquires the shape of the molding surface, the gripping element being actuated from its active configuration to its inactive configuration before said application of the shaping wall. during the positioning of the fibrous insert on the molding surface of the first part: bringing the fibrous insert closer to the molding surface of the first part while maintaining a separation between said molding surface and the fibrous insert; and moving the shaping wall relative to the gripping element so as to apply the fibrous insert against part of the molding surface; and during the shaping of the fibrous insert: applying the shaping wall and the gripping element against the fibrous insert and the molding surface of the first part, such that the fibrous insert acquires the shape of the molding surface, the gripping element being actuated from its active configuration to its inactive configuration before said application of the shaping wall.