The SIASP (public service employees information system) records the annual wages of every employee in the French public sector. Thanks to its exhaustive nature, it constitutes a particularly useful database for examining the gender pay gap. This article looks at the contribution of that pay gap to wage inequality among all employees in this sector. We take into consideration the total net pay received by each employee as the sum of several elements, one specific to his/her age representing the stage reached in the career, a second one determined by gender and a final one associated with other characteristics; we then evaluate the contribution of gender to wage inequality, measured by the Gini index, using a decomposition based on the Shapley value. This decomposition attributes to the gender pay gap a contribution of 10% for category A, 10.6% for category B and 11.7% for category C. Large disparities can be seen between the different segments of the public sector. In the hospital sector, the contribution of gender is very low in category A. However, in the state civil service, all categories show a gender contribution of above 10%, particularly in central civil service departments. In the territorial civil service, the proportion of wage inequality attributable to gender pay differences in greater in categories A and C than in category B, and also in other local public bodies compared to local government.