The molten salt reactor (MSR) flowing-fuel simulation capability of the Griffin-Pronghorn-coupled multiphysics code system developed by Idaho National Laboratory (INL) was verified against the Center National de la Recherche Scientifique (CNRS) MSR benchmark problem. Griffin and Pronghorn, which are INL’s neutronics and thermal-hydraulics codes built upon the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, have been recently extended to handle the flowing fuel of MSRs causing the drift of delayed neutron precursors (DNP). In the Griffin-Pronghorn code system, Griffin provides the fission rate density to Pronghorn, which simulates the generation, decay, and transport of DNPs along with the fluid, and the redistributed DNP densities are fed back to Griffin. The coupling and transfers are largely automatically managed at the framework level by the powerful MultiApp system of MOOSE. The verification results against the CNRS benchmark problem demonstrate that the Griffin-Pronghorn code system can accurately simulate the unique physics phenomena of MSRs in both steady-state and transient conditions.