Probabilistic seismic hazard assessment requires earthquake events characterized in terms of the moment magnitude (MW) scale both in the earthquake catalogues and in the ground-motion databases. These magnitudes can be either estimated directly after an inversion of the moment tensor or can be deduced from other magnitude scales using a scale conversion formula. However, for the same event, even its moment tensor based MW estimates provided by different agencies may differ due to differences in computation methods, inverted data or seismic networks – especially among small-moderate sized events. A few recent studies have shown that erroneous MW estimates may bias the magnitude-scaling of ground-motion in GMMs, and that merging of inhomogenous MW estimates leads to a larger ‘apparent’ between-event variability of the Ground-Motion Models [GMMs]. Various strategies have been adopted in the literature to define a unique, reference MW for each event in earthquake catalogues and ground-motion databases. Some strategies follow a priority scheme to prefer an Mw source over another, e.g. the European-Mediterranean Earthquake Catalogue. While others prefer to correct the Mw estimates of each source for their systematic deviation relative to an Mw reference source, and then average the available Mw estimates for each event, e.g. the Italian Catalogue. In this study, we first attempt such homogenisation of Mw in the French RESIF-RAP dataset, and then assess its impact on GMMs’ between-event variability. Since in low-moderate seismicity regions of Europe, small-moderate sized events significantly contribute to hazard estimates, it becomes critical that their MW estimates are homogenised prior to development of regional seismic source models and GMMs. We present the progress towards such homogenisation of Mw in the French context.