The NaMnF3 fluoride-perovskite has been found, theoretically, to be ferroelectric under epitaxial strain becoming a promising alternative to conventional oxides for multiferroic applications. Nevertheless, this fluoroperovskite has not been experimentally verified to be ferroelectric so far. Here we report signatures of room temperature ferroelectricity observed in perovskite NaMnF3 thin films grown on SrTiO3. Using piezoresponse force microscopy, we studied the evolution of ferroelectric polarization in response to external and built-in electric fields. Density functional theory calculations were also performed to help understand the strong competition between ferroelectric and paraelectric phases as well as the profound influences of strain. These results, together with the magnetic order previously reported in the same material, pave the way to future multiferroic and magnetoelectric investigations in fluoroperovskites.