There appears to be little doubt as to the existence of an intentional technological resolve to produce convergent tools during the Middle Palaeolithic. However, the use of these pieces as pointed tools is still subject to debate: i.e., handheld tool vs. hafted tool. Present-day technological analysis has begun to apply new methodologies in order to quantify shape variability and to decipher the role of the morphology of these pieces in relation to function; for instance, geometric morphometric analyses have recently been applied with successful results. This paper presents a study of this type of analysis on 37 convergent tools from level Ga of Payre site (France), dated to MIS 8-7. These pieces are non-standardized knapping products produced by discoidal and orthogonal core technologies. Moreover, macro-wear studies attest to various activities on diverse materials with no evidence of hafting or projectile use. The aim of this paper is to test the geometric morphometric approach on non-standardized artefacts applying the Elliptical Fourier analysis (EFA) to 3D contours and to assess the potential relationship between size and shape, technology and function. This study is innovative in that it is the first time that this method, considered to be a valuable complement for describing technological and functional attributes, is applied to 3D contours of lithic products. Our results show that this methodology ensures a very good degree of accuracy in describing shape variations of the sharp edges of technologically non-standardized convergent tools. EFA on 3D contours indicates variations in deviations of the outline along the third dimension (i.e., dorso-ventrally) and yields quantitative and insightful information on the actual shape variations of tools. Several statistically significant relationships are found between shape variation and use-wear attributes, though the results emphasize the large variability of the shape of the convergent tools, which, in general, does not show a strong direct association with technological features and function. This is in good agreement with the technological context of this chronological period, characterized by a wide diversity of non-standardized tools adapted to multipurpose functions for varied subsistence activities.