The state with a giant permittivity (ε′∼10⁴) and ferromagnetism have been observed above 185 K (including room temperature) in single crystals of diluted semiconductor manganite-multiferroic Eu_0.8Ce_0.2Mn₂O₅ in the investigations of x-ray diffraction, heat capacity, dielectric and magnetic properties, conductivity, and Raman light-scattering spectra of this material. X-ray diffraction study has revealed a layered superstructure along the c axis at room temperature. A model of the state with a giant ε′ including as-grown two-dimensional layers with doping impurities, charge carriers, and double-exchange-coupled Mn³⁺-Mn⁴⁺ ion pairs is suggested. At low temperatures these layers form isolated electrically neutral small-size one-dimensional superlattices, in which de Haas–van Alphen oscillations were observed. As temperature grows and hopping conductivity increases, the charge carrier self-organization in the crystal causes formation of a layered superstructure consisting of charged layers (with an excess Mn³⁺ concentration) alternating with dielectric layers of the initial crystal—the ferroelectricity due to charge-ordering state. Ferromagnetism results from double exchange between Mn³⁺ and Mn⁴⁺ ions by means of charge carriers in the charged layers. Temperature evolution of frequency shifts of A_g modes and quasielastic scattering in Raman-scattering spectra agree with the pattern of phase transitions in ECMO suggested.