Composites of carbons with metal oxides and metal sulfides have attracted a lot of interest as materials for energy conversion and storage applications. Herein, we report on novel N,O-doped carbon/ZnO/ZnS and N,O-doped carbon/ZnO composites (generally named C-(MOF-5/PANI)), synthesized by the carbonization of metal–organic framework MOF-5/polyaniline (PANI) composites. The produced C-(MOF-5/PANI)s are comprehensively characterized in terms of composition, molecular and crystalline structure, morphology, electrical conductivity, surface area, and electrochemical behavior. The composition and properties of C-(MOF-5/PANI) composites are dictated by the composition of MOF-5/PANI precursors and the form of PANI (conducting emeraldine salt (ES) or nonconducting emeraldine base). The ZnS phase is formed only with the PANI-ES form due to S-containing counter-ions. XRPD revealed that ZnO and ZnS existed as pure wurtzite crystalline phases. PANI and MOF-5 acted synergistically to produce C-(MOF-5/PANI)s with high SBET (up to 609 m2 g−1), electrical conductivity (up to 0.24 S cm−1), and specific capacitance, Cspec, (up to 238.2 F g−1 at 10 mV s−1). Values of Cspec commensurated with N content in C-(MOF-5/PANI) composites (1–10 wt.%) and overcame Cspec of carbonized individual components PANI and MOF-5. By acid etching treatment of C-(MOF-5/PANI), SBET and Cspec increased to 1148 m2 g−1 and 341 F g−1, respectively. The developed composites represent promising electrode materials for supercapacitors.