The recent seismicity catalogue of metropolitan France Sismicité Instrumentale de l’Hexagone (SI-Hex) covers the period 1962–2009. It is the outcome of a multipartner project conducted between 2010 and 2013. In this catalogue, moment magnitudes (Mw) are mainly determined from short-period velocimetric records, the same records as those used by the Laboratoire de Détection Géophysique (LDG) for issuing local magnitudes (ML) since 1962. Two distinct procedures are used, whether ML-LDG is larger or smaller than 4. For ML-LDG >4, Mw is computed by fitting the coda-wave amplitude on the raw records. Station corrections and regional properties of coda-wave attenuation are taken into account in the computations. For ML-LDG ≤4, Mw is converted from ML-LDG through linear regression rules. In the smallest magnitude range ML-LDG <3.1, special attention is paid to the non-unity slope of the relation between the local magnitudes and Mw. All Mw determined during the SI-Hex project is calibrated according to reference Mw of recent events. As for some small events, no ML-LDG has been determined; local magnitudes issued by other French networks or LDG duration magnitude (MD) are first converted into ML-LDG before applying the conversion rules. This paper shows how the different sources of information and the different magnitude ranges are combined in order to determine an unbiased set of Mw for the whole 38,027 events of the catalogue.