We investigate recordings from weak to moderate earthquakes, with magnitudes ranging between about 3 and 5, recorded by the French Accelerometric Network. S-wave spectra are modelled as a product of source, propagation and site terms. Inverting large data sets of multiple earthquakes recorded at multiple stations allows us to separate the three contributions. Source parameters such as moment magnitude, corner frequency and stress drop are estimated for each earthquake. We provide the first complete and homogeneous catalogue of moment magnitudes for France, for the events with magnitude greater than 3 that occurred between 1996 and 2006. Stress drops are found to be regionally dependent as well as magnitude dependent, and range from about 0.1 MPa (1 bar) to about 30 MPa (300 bars). The attenuation parameters show that, in France on a nationwide scale, variations of attenuation properties do exist. Site transfer functions are also computed, giving the level of amplification at different frequencies with respect to the response of a generic rock site (characterized by an average 30 m S-wave velocity, vs30, of 2000ms-1). From these site terms, we compute the high-frequency fall-off parameter κ [modelled as exp (-πκf), with f the frequency] for 76 stations. We also determine rock stations vs30 and we show the κ-vs30 relationship for 21 rock stations.