On March 17, 2020, French authorities implemented a nationwide lockdown to respond to COVID-19 epidemic emergency and curb the surge of patients requiring critical care, similarly to other countries. Evaluating the impact of lockdown on population mobility is important to help characterize the changes in social dynamics that affected viral diffusion. Using travel flows reconstructed from mobile phone trajectories, we measured how lockdown altered mobility patterns at both local and country scales. Lockdown caused a 65% reduction in countrywide number of displacements, and was particularly effective in reducing work-related short-range mobility, especially during rush hours, and recreational long-range trips. Anomalous increases in long-range movements, localized in both time and space, emerged even before lockdown announcement. Mobility drops were unevenly distributed across regions. They were strongly associated with active population, workers employed in sectors highly impacted by lockdown, and number of hospitalizations per region, and moderately associated with socio-economic level of the region. Major cities largely shrank their pattern of connectivity, reducing it mainly to short-range commuting, despite the persistence of some long-range trips. Our findings indicate that lockdown was very effective in reducing population mobility across scales. Caution should be taken in the timing of policy announcements and implementation. Individual response to policy announcements may generate unexpected anomalous behaviors increasing the risk of geographical diffusion. On the other hand, risk awareness may be beneficial in further decreasing mobility in largely affected regions. Our findings help predicting how and where restrictions will be the most effective in reducing the mobility and mixing of the population, thus aiding tuning recommendations in the upcoming weeks, when phasing out lockdown.