An angle sensor based on multiple beam interference of a Fabry-Pérot etalon employing a mode-locked femtosecond laser as the measurement beam is proposed. Output angles are evaluated by using estimated local maxima within a measurement bandwidth of an output fringe spectrum detected by an optical spectrum analyzer. In the proposed method, fringe spectra produced by beams from transmittance and a reflectance side of the Fabry-Pérot etalon are detected individually, and intensities of two spectra are divided to increase the visibility by narrowing a spectrum width. Confirmation of an increase in the visibility is conducted by comparing full width half maximum values of spectra obtained by a constructed optical setup, and evaluation accuracies were compared by repeating measurements for 100 times. The output angle using estimated local maxima of the divided spectra is then evaluated to verify the feasibility of the proposed method. As a result, it is confirmed that the proposed method improves the accuracy of angle determination by one order of magnitude.