The 2D conjugated coordination polymer frameworks (2D c‐CPFs), as a novel class of electronic materials, show significant potential in modern electronic devices. However, the lack of available construction monomers greatly hinders the development as well as the fundamental electronic process understanding of 2D c‐CPF in modern electronics. Herein, a novel conjugated coordination polymer framework is developed through coordination of a new planar ligand with copper ions. Benefiting from the in‐plane d–π conjugation and out‐of‐plane π stacking, as‐made coordination polymer framework exhibits a narrow bandgap of 1.12 eV. Then, a free‐standing hybrid layered film of coordination frameworks together with exfoliated graphene is prepared as the electrode for micro‐supercapacitors. The micro‐device displays the high areal specific capacitance of 14.3 mF cm−2, outperforming most of the reported conductive polymer‐based micro‐supercapacitors. Notably, the as‐prepared micro‐supercapacitor exhibits good electrochemical stability after 5000 cycles, as well as excellent flexibility for polyethylene terephthalate‐supported devices. Herein, not only is a novel d–π conjugated coordination polymer with narrow bandgap developed, but also its application in miniature and flexible devices is identified.