The present constraint on the space parity P and time-reflection invariance T violating the electron electric dipole moment (eEDM) is based on the observation of the electron-spin precession in an external electric field using the ThO molecule. We propose an alternative approach: observation of the P,T-odd Faraday effect in an external electric field using the cavity-enhanced polarimetric scheme in combination with a molecular beam crossing the cavity. Our theoretical simulation of the proposed experiment with the PbF and ThO molecular beams shows that the present constraint on the eEDM in principle can be improved by a few orders of magnitude.