Bike sharing systems (BSSs) have become a mean of sustainable intermodal transport and are now proposed in many cities worldwide. Most of BSSs also provide an open access to their data, through APIs, and in particular an access to real time status reports on their bike stations. The analysis of the data generated by such systems is of particular interest for BSS providers, researchers in social sciences and even users. This work was motivated by the analysis and the comparison of several European BSSs. To this end, a model-based clustering method, called FunFEM, for time series (or more generally functional data) is developed. It is based on a discriminative functional mixture model which allows the clustering of the data in a functional subspace. This model presents the advantage to be parsimonious and can therefore handle long time series. Numerical experiments confirm the good behavior of FunFEM, in particular compared to state-of-the-art methods. The application of FunFEM to BSS data from JCDecaux and Transport for London Initiative provides insightful analyses on the Vélib system and informative comparisons between 8 European BSSs.