Seasonal waves of influenza display a complex spatiotemporal pattern resulting from the interplay of biological, sociodemographic, and environmental factors. At country level many studies characterized the robust properties of annual epidemics, depicting a typical season. Here we analyzed season-by-season variability, introducing a clustering approach to assess the deviations from typical spreading patterns. The classification is performed on the similarity of temporal configurations of onset and peak times of regional epidemics, based on influenza-like-illness time-series in France from 1984 to 2014. We observed a larger variability in the onset compared to the peak. Two relevant classes of clusters emerge: groups of seasons sharing similar recurrent spreading patterns (clustered seasons) and single seasons displaying unique patterns (monoids). Recurrent patterns exhibit a more pronounced spatial signature than unique patterns. We assessed how seasons shift between these classes from onset to peak depending on epidemiological, environmental, and socio-demographic variables. We found that the spatial dynamics of influenza and its association with commuting, previously observed as a general property of French influenza epidemics, apply only to seasons exhibiting recurrent patterns. The proposed methodology is successful in providing new insights on influenza spread and can be applied to incidence time-series of different countries and different diseases.