Structure for fastening a front wing of a motor vehicle, comprising rigid bodywork elements to which said front wing is fastened, said bodywork elements comprising: - a reinforcement extending towards the front of the vehicle and comprising an upper edge extending substantially parallel to an upper edge of the front wing, which upper edge is prolonged downwardly by a border, with the result that the upper part of the front wing has a substantially U-shaped cross section, said border being spaced from the upper edge of the reinforcement, - a support element, closing the space thus defined, fastened to the border of the front wing by a substantially vertical first face, and to said upper edge of the reinforcement by a substantially horizontal second face, with the result that the support element has an L-shaped cross section, said support element comprising stiffening means (7, 8) ensuring the stiffness of the front wing and additional stiffening means (17, 18, 19) arranged on said substantially horizontal face of the support element so as to transversely stiffen the front wing without preventing the deformation thereof in the event of a "pedestrian impact"-type impact, said additional stiffening means of the support element comprise: - a first shaping arranged at the junction between said substantially vertical face and said substantially horizontal face, - two transverse ribs arranged over the whole width of said substantially horizontal face of the support element and in a substantially central region of the support element, which structure is characterized in that the first shaping is arranged in a substantially front region of the support element, and in that said additional stiffening means comprise - a second shaping of triangular shape arranged on said substantially horizontal face of the support element and between said two transverse ribs of the support element. - a reinforcement extending towards the front of the vehicle and comprising an upper edge extending substantially parallel to an upper edge of the front wing, which upper edge is prolonged downwardly by a border, with the result that the upper part of the front wing has a substantially U-shaped cross section, said border being spaced from the upper edge of the reinforcement, - a support element, closing the space thus defined, fastened to the border of the front wing by a substantially vertical first face, and to said upper edge of the reinforcement by a substantially horizontal second face, with the result that the support element has an L-shaped cross section, said support element comprising stiffening means (7, 8) ensuring the stiffness of the front wing and additional stiffening means (17, 18, 19) arranged on said substantially horizontal face of the support element so as to transversely stiffen the front wing without preventing the deformation thereof in the event of a "pedestrian impact"-type impact, - a first shaping arranged at the junction between said substantially vertical face and said substantially horizontal face, - two transverse ribs arranged over the whole width of said substantially horizontal face of the support element and in a substantially central region of the support element, - a second shaping of triangular shape arranged on said substantially horizontal face of the support element and between said two transverse ribs of the support element.