Highly conductive carbon-based fibrous composites have become one of the most sought-after components in the field of electromagnetic interference (EMI) shielding due to their excellent comprehensive performance. In this work, a flexible nonwoven fabric consisting of carbon fibers (CFs) and polypropylene/polyethylene (PP/PE) core/sheath bicomponent fibers (ESFs), known as CEF-NF, is introduced into the graphene (GE)/poly(vinylidene fluoride) (PVDF) nanocomposite obtained by a solution casting method to fabricate a CEF-NF/GE/PVDF film. Disparate microstructures can be clearly observed in CEF-NF/GE/PVDF films with different graphene contents. Thanks to an internal porous network structure formed when the graphene content is high, this film exhibits better electrical conductivity. In the frequency range of 30-1500 MHz, this film can achieve a significantly high EMI shielding effectiveness (EMI-SE) value of about 48.5 dB at tiny thickness and density (1731.40 dB cm2 g-1), which are far better than many competitive materials. Moreover, this film exhibits adequate tensile strength and excellent flexibility, as the film's structural form can be retained even after multiple folding processes. In addition, by combining two-dimensional (2D) graphene and one-dimensional (1D) CF, the CEF-NF/GE/PVDF film achieves a remarkable in-plane thermal conductivity of 25.702 W m-1 K-1, making it an exceptional heat conductor. In summary, our results demonstrate that CEF-NF/GE/PVDF film is an excellent EMI shielding material that is light weight, highly flexible, and mechanically robust with outstanding thermal conductivity, which positions it superbly for applications in next-generation commercial portable electronics.