Herein, we design and implement a laser frequency stability measurement system based on coherent detection and Rayleigh scattering to measure the instantaneous small frequency deviation of the laser. Based on the proposed system, the study examines performance degradation due to laser frequency fluctuation in distributed Brillouin sensors. Results show that large frequency fluctuation of the laser can result in the broadening of the Brillouin gain spectrum and deviation from the Lorentz shape. This produces a large error in the measurement of Brillouin frequency and limits the sensing range to 15 km for the laser studied. The sensing range can be extended to 50 km by a laser with good frequency stability.