In this work a new superstructured, in-fiber Bragg grating (FBG)-based, contact force sensor is presented that is based on birefringent D-shape optical fiber. The sensor superstructure comprises a polyimide sheath, a stress-concentrating feature, and an alignment feature that repeatably orients the sensor with respect to contact forces. A combination of plane elasticity and strain-optic models is used to predict sensor performance in terms of sensitivity to contact force and axial strain. Model predictions are validated through experimental calibration and indicate contact force, axial strain, and temperature sensitivities of $169.6\mathrm{pm}/(\mathrm{N}/\mathrm{mm})$, $0.01\mathrm{pm}/\mu \epsilon$, and $-1.12\mathrm{pm}/°\mathrm{C}$ in terms of spectral separation. The sensor addresses challenges associated with contact force sensors that are based on FBGs in birefringent fiber, FBGs in conventional optical fiber, and tilted FBGs. Relative to other birefringent fiber sensors, the sensor has contact force sensitivity comparable to the highest sensitivity of commercially available birefringent fibers and, unlike other birefringent fiber sensors, is self-aligning with respect to contact forces. Unlike sensors based on Bragg gratings in conventional fiber and tilted Bragg gratings, the sensor has minimal cosensitivity to both axial strain and changes in temperature.