The title reaction and its deuterated analogue (ND3 + F-->ND2 + FD) were studied by means of an analytical expression for their potential energy surface. The analytical form is the one previously used for the similar NH3 + H --> NH2 + H-2 reaction. As calibration criteria, we used the reactant and product experimental properties and the theoretically calculated properties of a hydrogen-bonded complex linking NH2 and FH. Using this potential energy surface, we analyzed the effects of the reaction path curvature (translation-vibration coupling) in order to explain the low vibrational excitation observed for the FH product, as a result of the compensation between the effects of the reaction path curvature and the randomization of the energy favored by the deep hydrogen-bonded well. Variational transition state theory was used to calculate the rate constants for the title reaction and the kinetic isotope effects over the temperature range 100-500 K, finding that anharmonic effects are very important: they lower the rate constants by a fatter of about 200 and make the agreement between our theoretical values and the experimental estimates reasonable. Finally, our results were compared with those obtained by means of the simple Gorin model that yields values very close to the experimental measurements.