A combined study of the structural and electronic properties of polycrystalline Pu_2C_3 is reported based on x-ray diffraction, specific heat, magnetic susceptibility, ^13C nuclear magnetic resonance (NMR), and band structure calculations. X-ray diffraction reveals a global noncentrosymmetric cubic lattice, with a nearest-neighbor C--C bond length of r = 1.38 Å. ^13C NMR measurements indicate that the global cubic symmetry is locally broken, revealing two unique carbon environments. Magnetic susceptibility suggests enhanced Pauli paramagnetism, and specific heat reveals a moderately large electronic Sommerfeld coefficient γ= 45 mJ mol_\mathrmPu^-1 K^-2, with a Wilson ratio R_W ≈ 1.3 further indicating moderate correlations. ^13C nuclear spin-lattice relaxation rate (1/T_1) and Knight shift (K) measurements find metallic Korringa behavior (i.e., T_1TK^2= const.) with modest ferromagnetic spin fluctuations at low temperature. Taken together, the data point to a delocalized nature of a narrow 5f-electron band with weak electronic correlations. Density functional theory band-structure calculations confirm the appearance of such narrow 5f bands near the Fermi level. Our data provide prime evidence for a plutonium-based metallic system with weak electronic correlations, which sheds new light on the understanding of complex paramagnetism in actinide-based metallic compounds.