In this paper, chirped fiber Bragg gratings (CFBGs) with tunable parameters are successfully fabricated in fluorotellurite fiber (FTF) using the femtosecond laser point-by-point method combined with slit beam shaping technique. By precisely controlling the processing parameters, CFBGs with adjustable bandwidths (3–9 nm) and center wavelengths (3.5–3.7 μm) are realized, and the highest reflectivity is 99%. The fabricated CFBGs demonstrate good temperature response characteristics from room temperature to 400°C, with a temperature sensitivity of 39.47 pm/°C. This study first achieves flexible fabrication of mid-infrared CFBGs in FTF using the femtosecond laser point-by-point method, providing critical device support for the development of mid-infrared fiber lasers and demonstrating significant application value.