A continuous-energy sensitivity coefficient calculation to nuclear data capability has been recently developed in Version 5.C.1 of the MORET Monte Carlo code developed at Institut de Radioprotection et de Sûreté nucléaire (IRSN). The method used for implementation is the differential operator method. In this method, the estimation of the fission source derivatives is replaced by an estimation of the adjoint flux. Both methodology and tallies are described in this paper. The preliminary verification is mainly performed using code-to-code comparisons with the SCALE6.1 and MCNP6.1 software packages. Configurations used for verification are the Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) Uncertainty Analyses for Criticality Safety Assessment (UACSA) Expert Group benchmarks, the Jezebel International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmark, and a configuration from the Matériaux en Interaction et Réflexion Toutes Epaisseurs (MIRTE) French proprietary experimental program. Results show good agreement among the different codes.