A coupling device, which can extract coherent edge radiation (CER) from an optical cavity for a free-electron laser (FEL) without damaging the FEL due to diffraction loss, was developed at Nihon University. We successfully observed the CER beam with a power of 1 mW or more in the terahertz range during FEL oscillation. It is revealed that the CER power changed with the detuning of the optical cavity and the dependence of the CER power on the detuning length differs from that of the FEL power. The measured CER spectra indicate that the longitudinal electron distribution in a bunch is modulated by the FEL oscillation with a period corresponding to the FEL slippage length. We herein report the characteristics of the CER with FEL oscillation in detail. These results demonstrate that the CER is excellent tool to reveal the overall effect of FEL interaction on electron distribution in a bunch.