This paper focuses on three main issues regarding Material Extrusion (MEX) Additive Manufacturing (AM) of thermoplastic composites reinforced by pre-functionalized continuous Nickel–Titanium (NiTi) wires: (i) Evaluation of the effect of the MEX process on the properties of the pre-functionalized NiTi, (ii) evaluation of the mechanical and thermal behavior of the composite material during usage, (iii) the inspection of the parts by Non-Destructive Testing (NDT). For this purpose, an optical fiber sensing network, based on fiber Bragg grating and a cascaded optical fiber sensor, was successfully embedded during the 3D printing of a polylactic acid (PLA) matrix reinforced by NiTi wires. Thermal and mechanical perturbations were successfully registered as a consequence of thermal and mechanical stimuli. During a heating/cooling cycle, a maximum contraction of ≈100 µm was detected by the cascaded sensor in the PLA material at the end of the heating step (induced by Joule effect) of NiTi wires and a thermal perturbation associated with the structural transformation of austenite to R-phase was observed during the natural cooling step, near 33.0 °C. Regarding tensile cycling tests, higher increases in temperature arose when the applied force ranged between 0.7 and 1.1 kN, reaching a maximum temperature variation of 9.5 ± 0.1 °C. During the unload step, a slope change in the temperature behavior was detected, which is associated with the material transformation of the NiTi wire (martensite to austenite). The embedded optical sensing methodology presented here proved to be an effective and precise tool to identify structural transformations regarding the specific application as a Non-Destructive Testing for AM.