We theoretically study the spectral characteristics and noise performance of wavelength-interrogated fiber-optic sensors based on an extrinsic Fabry-Perot (FP) interferometer (EFPI) formed by thin metal mirrors. We develop a model and use it to analyze the effect of key sensor parameters on the visibility and spectral width of the sensors, including the beam width of the incident light, metal coating film thickness, FP cavity length, and wedge angle of the two mirrors. Through Monte Carlo simulations, we obtain an empirical equation that can be used to estimate the wavelength resolution from the visibility and spectral width, which can be used as a figure-of-merit that is inherent to the sensor and independent on the system noises. The work provides a useful tool for designing, constructing, and interrogating high-resolution fiber-optic EFPI sensors.