It has been proposed to measure the electric dipole moment of the electron on the basis of the observation of the P-, T-odd Faraday effect on a molecular beam intersecting a cavity using cavity-enhanced intracavity laser absorption spectroscopy. The effective electric field acting on the electric dipole moment of the electron, as well as the molecular parameter of the scalar-pseudoscalar nucleus-electron interaction, has been calculated for the ground and excited electronic states of the lead monofluoride molecule. The simulation of the experiment has shown that the proposed approach allows improving the current bounds on the electric dipole moment of the electron and the scalar-pseudoscalar nucleus-electron interaction constant by six orders of magnitude.