The French National Center for Scientific Research (CNRS) is carrying out design studies on a nuclear electric propulsion (NEP) engine based on a molten salt reactor (MSR). A NEP engine based on liquid nuclear fuel could allow developing a core design with relatively high power densities and temperatures while using simple reactivity control systems and keeping low pressure and temperature gradients in the fuel. Nevertheless, the design work of such an engine poses significant technical challenges and requires the use of advanced numerical simulation tools. Different MSRs for space are currently being studied. In this work, a MSR concept using a fast neutron spectrum is investigated using a multiphysics tool based on a numerical coupling between the OpenFOAM (computational fluid dynamics) and SERPENT 2 (Monte Carlo neutronics) codes. The analysis of this paper is focused on the reactor core coupled neutronic and thermal-hydraulic phenomena. Steady state full-power conditions are calculated for two different fast MSR designs using low-enriched uranium (LEU) and highly enriched uranium. The results show that the proposed core layout and materials allow obtaining a satisfactory temperature distribution in the core (maximal values and gradients) without significant penalization of the reactor operating conditions. A reactivity control strategy excluding the use of control rods is studied for the LEU concept. Transient and safety studies are also performed and show acceptable performance.