This study firstly proposes and experimentally demonstrates a phase demodulation method with high sensitivity for interferometric fiber sensors (IFSs) on the basis of the fast Fourier transform of a wavenumber domain. The phase information of IFSs triggered by changes in environmental parameters is obtained by calculating the initial phase variation of a specific Fourier-transformed spatial frequency. Theoretically, phase sensitivity can be improved by n times when the optical path difference (OPD) of a spatial frequency peak is increased by a multiple (n times) of the OPD of other spatial frequency domain peaks. To verify the method experimentally, this study designed a large laterally offset spliced sensor formed by common singlemode fibers on the basis of mode interference. The sensing characteristics of temperature and strain in each set of two-beam interference are analyzed simultaneously by calculating the phase sensitivities of the frequency domain peaks. Furthermore, the highest reported temperature and strain sensitivities of 0.0795 rad/°C and −0.0088 rad/με, respectively, with good repeatability are realized.