Ground‐motion prediction equations (GMPE) are essential in probabilistic seismic hazard studies for estimating the ground motions generated by the seismic sources. In low‐seismicity regions, only weak motions are available during the lifetime of accelerometric networks, and the equations selected for the probabilistic studies are usually models established from foreign data. Although most GMPEs have been developed for magnitudes 5 and above, the minimum magnitude often used in probabilistic studies in low‐seismicity regions is smaller. Disaggregations have shown that, at return periods of engineering interest, magnitudes less than 5 may be contributing to the hazard. This paper presents the testing of several GMPEs selected in current international and national probabilistic projects against weak motions recorded in France (191 recordings with source–site distances up to 300 km, 3.8≤Mw≤4.5). The method is based on the log‐likelihood value proposed by Scherbaum et al. (2009). The best‐fitting models (approximately 2.5≤LLH≤3.5) over the whole frequency range are the Cauzzi and Faccioli (2008), Akkar and Bommer (2010), and Abrahamson and Silva (2008) models. No significant regional variation of ground motions is highlighted, and the magnitude scaling could be the predominant factor in the control of ground‐motion amplitudes. Furthermore, we take advantage of a rich Japanese dataset to run tests on randomly selected low‐magnitude subsets, and confirm that a dataset of ∼190 observations, the same size as the French dataset, is large enough to obtain stable LLH estimates. Additionally we perform the tests against larger magnitudes (5–7) from the Japanese dataset. The ranking of models is partially modified, indicating a magnitude scaling effect for some of the models, and showing that extrapolating testing results obtained from low‐magnitude ranges to higher magnitude ranges is not straightforward.