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In this study, a polyvinylidene fluoride (PVDF)/graphene nanoplatelet (GNP) micro-nanocomposite membrane was fabricated through electrospinning technology and was employed in the fabrication of a fiber-reinforced polymer composite laminate. Some glass fibers were replaced with carbon fibers to serve as electrodes in the sensing layer, and the PVDF/GNP micro-nanocomposite membrane was embedded in the laminate to confer multifunctional piezoelectric self-sensing ability. The self-sensing composite laminate has both favorable mechanical properties and sensing ability. The effects of different concentrations of modified multiwalled carbon nanotubes (CNTs) and GNPs on the morphology of PVDF fibers and the β-phase content of the membrane were investigated. PVDF fibers containing 0.05% GNPs were the most stable and had the highest relative β-phase content; these fibers were embedded in glass fiber fabric to prepare the piezoelectric self-sensing composite laminate. To test the laminate’s practical application, four-point bending and low-velocity impact tests were performed. The results revealed that when damage occurred during bending, the piezoelectric response changed, confirming that the piezoelectric self-sensing composite laminate has preliminary sensing performance. The low-velocity impact experiment revealed the effect of impact energy on sensing performance.