The ideal development direction of the fiber-optic acoustic sensor (FOAS) is toward broadband, a high sensitivity and a large dynamic range. In order to further promote the acoustic detection potential of the Fabry–Pérot etalon (FPE)-based FOAS, it is of great significance to study the acoustic performance of the FOAS with the quality (Q) factor of FPE as the research objective. This is because the Q factor represents the storage capability and loss characteristic of the FPE. The three FOASs with different Q factors all achieve a broadband response from 20 Hz to 70 kHz with a flatness of ±2 dB, which is consistent with the theory that the frequency response of the FOAS is not affected by the Q factor. Moreover, the sensitivity of the FOAS is proportional to the Q factor. When the Q factor is 1.04×106, the sensitivity of the FOAS is as high as 526.8 mV/Pa. Meanwhile, the minimum detectable sound pressure of 347.33 μPa/Hz1/2 is achieved. Furthermore, with a Q factor of 0.27×106, the maximum detectable sound pressure and dynamic range are 152.32 dB and 107.2 dB, respectively, which is greatly improved compared with two other FOASs. Separately, the FOASs with different Q factors exhibit an excellent acoustic performance in weak sound detection and high sound pressure detection. Therefore, different acoustic detection requirements can be met by selecting the appropriate Q factor, which further broadens the application range and detection potential of FOASs.