This paper analyzes the cost structure of the French electricity distribution sector prior to the re-structuring reforms that have been initiated in 2005 and gradually implemented in the form of re-grouping certain activities across distribution units. The aim of this study is to assess the empirical evidence in support of these re-structuring measures. We explore the cost structure of the distribution units operating in France over the three year period. The data include 279 observations from 93 distribution units from 2003 to 2005, operating within the French electricity distribution network namely, Electricité Réseau Distribution France (ERDF). A Cobb-Douglas cost function is estimated using several specifications focusing on the analysis of the economies of scale and customer density. In order to account for the unobserved heterogeneity and its impacts on the economies of scale, we use a latent class specification. The results suggest that a majority of the distribution units can exploit statistically significant economies of scale. Further, the empirical analysis indicates that the unexploited economies of scale can vary considerably from one unit to another, not only because of variations in outputs but also because of the unobserved differences in networks and technological characteristics. In particular, the latent class approach can identify a group of distribution units that do not show any significant economies of scale. Further analysis suggests that such distributors are often located in metropolitan areas with high customer density.