Plasmonic hot-carrier-based photodetectors detect light at frequencies below the semiconductor bandgap with room temperature operation and can exhibit spectrally narrowband behavior, potentially eliminating the need for bulky filtering or dispersive optics. This photodetection mechanism has, however, been plagued with low responsivities. Here we combine hot-carrier-based photodetection with free-carrier absorption (FCA) in highly doped p-type Si to create a narrowband, near-infrared, photodetector architecture with enhanced performance. By fabricating Au and Pd gratings on a p-type Si substrate, >1 A/W responsivities were obtained at the relatively low biases of 275 and 93 mV, respectively, with the minimum noise equivalent power <10 pW/√Hz in each case. This performance brings plasmonic, near-infrared, Si-based photodetectors nearly comparable to commercially available, non-Si-based, near-infrared photodetectors.