In this study, fennel (Foeniculum vulgare) seeds were used as a precursor to obtain carbon adsorbents through physical activation with carbon dioxide and chemical activation by impregnating the precursor with sodium carbonate. The physical activation involved the carbonization of the precursor at a temperature of 600 °C for 60 min and activation at a temperature of 800 °C for 30 min with carbon dioxide. Chemical activation included impregnation of the precursor with sodium carbonate at a mass ratio of a precursor to activator of 1:2. The mixture was activated in a nitrogen atmosphere with a flow rate at a temperature of 700 °C for 45 min. The resulting biochar samples were washed with 5% hydrochloric acid and subsequently rinsed with boiling distilled water. The biochar adsorbents were characterized using low-temperature nitrogen adsorption–desorption isotherms, Boehm titration, and pH measurements of their aqueous extracts. The specific surface area of the obtained adsorbents ranged from 89 to 345 m2/g. Biochar adsorbents exhibit a predominance of acidic groups over basic groups on their surfaces. The sorption capacities of the obtained samples towards an aqueous solution of methyl red range from 26 to 135 mg/g. Based on adsorption studies, it was found that the adsorption of the dye on the obtained biochar materials follows a pseudo-second-order model. The Freundlich isotherm best describes the studied process, indicating the formation of a multilayer of adsorbate on the adsorbent surface. The efficacy of adsorption in aqueous solutions of methyl red was found to increase with the elevation of the process temperature. Moreover, thermodynamic studies have shown that the adsorption process is spontaneous and endothermic. Consequently, this work provides a description of the physicochemical parameters of two biochars obtained by physical and chemical activation of a little-studied precursor—fennel seeds—and studies on their potential use as adsorbents for contaminants from the aqueous phase.