Nowadays, drinking water utilities need an acute comprehension of the water demand on their distribution network, in order to efficiently operate the optimization of resources, manage billing and propose new customer services. With the emergence of smart grids, based on automated meter reading (AMR), a better understanding of the consumption modes is now accessible for smart cities with more granularities. In this context, this paper evaluates a novel methodology for identifying relevant usage profiles from the water consumption data produced by smart meters. The methodology is fully data-driven using the consumption time series which are seen as functions or curves observed with an hourly time step. First, a Fourier-based additive time series decomposition model is introduced to extract seasonal patterns from time series. These patterns are intended to represent the customer habits in terms of water consumption. Two functional clustering approaches are then used to classify the extracted seasonal patterns: the functional version of K-means, and the Fourier REgression Mixture (FReMix) model. The K-means approach produces a hard segmentation and K representative prototypes. On the other hand, the FReMix is a generative model and also produces K profiles as well as a soft segmentation based on the posterior probabilities. The proposed approach is applied to a smart grid deployed on the largest water distribution network (WDN) in France. The two clustering strategies are evaluated and compared. Finally, a realistic interpretation of the consumption habits is given for each cluster. The extensive experiments and the qualitative interpretation of the resulting clusters allow one to highlight the effectiveness of the proposed methodology.