Plasmonic tilted fiber Bragg gratings (TFBGs) are very efficient for fast, accurate, and minimally invasive biosensing. Their transmitted amplitude spectrum is a dense comb of narrowband cladding mode resonances (full width at half maximum < 1 nm) that is usually demodulated using highly resolved (wavelength resolution < 10 pm) devices. This work demonstrates the possibility of using a coarsely resolved spectrometer (166 pm) to read out the amplitude spectrum of a gold-coated TFBG. A refined analysis of the spectral content has allowed us to develop signal processing that provides a refractometric sensitivity of 2656 nm/RIU. This is a fivefold improvement compared to previously reported read-out techniques. Biosensing has then been successfully implemented with gold-coated TFBGs implemented in reflection mode for the detection of insulin, with specific antibodies grafted on the gold surface. Our experimental work is a first step toward the industrialization of the FBG technology, as it opens the door to fast parallel biosensing, profiting from the multiple sensing channels (up to 64) of the interrogator and its high processing speed (repetition rate up to 3 kHz).