We present a novel high-sensitivity broad free-spectral-range (FSR) two-dimensional three-slot photonic crystal sensor integrated with a 1D photonic crystal tapered nanobeam bandgap filter (1DPC-TNBF) based on thin-film silicon. Designed to lie in the wavelength at around 1550 nm, the resonance of the two-dimensional photonic crystal three-slot cavity (2DPC-TSC) shows strong light-matter interaction in the slot region, which enhances the bulk refractive index sensitivity of the sensor significantly. The simulated sensitivity is over 900 nm/refractive index unit (RIU). By connecting an additional 1DPC-TNBF to a 2DPC-TSC in series, the high-order modes are suppressed, which means only a fundamental mode exists with a broad FSR over 200 nm. Thus, the proposed structure is promising in designing lab-on-a-chip applications, especially in compact parallel-integrated sensor arrays.