A system enabling the attachment of an object to an element (1) having attachment groove(s), having at least one grooved surface (2) including at least one attachment groove whose mouth (3) is defined longitudinally by two opposing edges (5) that each include an inner salient angle, the system includes an attachment device (6, 7), the element (1), and elements for coupling (8) with the object. The attachment device includes a clamping assembly and a locking element (7) capable of being at least partially inserted in the groove, directly in any of the attachment points along the latter, the assembly being at least partially resiliently or plastically deformable when exposed to a pressure bias exerted by the locking element in order to form, by deforming the material, an anchoring and clamping element capable of anchoring under the edges (5) and/or against the salient angles.