The idea of using mobile phone data to understand the impact of the Covid-19 pandemic and that of the sanitary constraints associated with it on human mobility imposed itself as evidence in most countries. This work uses spatiotemporal aggregated mobile phone data provided by a major French telecom operator, covering a geographical region centered on Paris for early 2020, i.e., periods before and during the first French lockdown. An essential property of this data is its fine-grained spatial resolution, which, to the best of our knowledge, is unique in the COVID-related mobility literature. Contrarily to regions or country-wide resolution, it describes population mobility flows among zones ranging from 0.025 km2 to 5.40 km2 , corresponding to 326 aggregated zones over the total area of 93.76 km2 of the city of Paris. We perform a data-driven mobility investigation and modeling to quantify (in space and time) the population attendance and visiting flows in different urban areas. Second, when looking at periods both before and during the lockdown, we quantify the consequences of mobility restrictions and decisions on an urban scale. For this, per zone, we define a so-called signature, which captures behaviors in terms of population attendance in the corresponding geographical region (i.e., their land use) and allows us automatically detect activity, residential, and outlier areas. We then study three different types of graph centrality, quantifying the importance of each zone in a time-dependent weighted graph according to the habits in the mobility of the population. Combining the three centrality measures, we compute per zone of the city, its impact-factor, and employ it to quantify the global importance of zones according to the population mobility. Our results firstly reveal the population's daily zone preferences in terms of attendance and mobility, with a high concentration on business and touristic zones. Second, results show that the lockdown mobility restrictions significantly reduced visitation and attendance patterns on zones, mainly in central Paris, and considerably changed the mobility habits of the population. As a side effect, most zones identified as mainly having activity-related population attendance in typical periods became residential-related zones during the lockdown, turning the entire city into a residential-like area. Shorter distance displacement restrictions imposed by the lockdown increased visitation to more "local" zones, i.e., close to the population's primary residence. Decentralization was also favored by the paths preferences of the still-moving population. On the other side, "jogging activities" allowing people to be outside their residences impacted parks visitation, increasing their visitation during the lockdown. By combining the impact factor and the signatures of the zones, we notice that areas with a higher impact factor are more likely to maintain regular land use during the lockdown.