This paper presents a novel approach to dual-frequency comb generation utilizing a single fiber Fabry–Perot resonator, advancing the implementation of these sources in fiber-based systems. Dual-comb applications such as spectroscopy, ranging, and imaging, known for their high-resolution and rapid data acquisition capabilities, benefit significantly from the stability and coherence of optical frequency comb sources. Our method leverages the birefringent property of the resonator induced by the optical fiber to generate two orthogonally polarized optical frequency combs in a monolithic resonator. This approach allows for the generation of two different frequency combs with slightly different repetition rates, exhibiting excellent mutual coherence, making it highly relevant for dual-comb applications. The 40 nm bandwidth generated combs are induced by switching-waves in a normal dispersion fiber Fabry-Perot resonator. These comb types have the advantage of being easily generated by a pulse pumping scheme, which is employed in this study. Finally, the potential of the source is demonstrated by a proof-of-concept spectroscopy measurement.