Synthetic polymer coatings impact the biodegradable behavior of cellulosic packaging material. The environmental consequences of food packaging disposal have increased consumer concern. The present study aimed to use natural polymer coatings incorporating palmitic acid and activated carbon applied to paperboard surfaces as a sustainable alternative to improve cellulosic packaging material’s moisture and fat barrier properties, minimizing the environmental impact. The coating formulation was defined using a Factorial Experimental Design with independent variables: chitosan, palmitic acid, activated carbon concentrations, and the number of coating layers. The highest concentration of chitosan (2.0% w/w) filled the pores of the cellulosic paperboard network, supporting the compounds incorporated into the filmogenic matrix and improving the fat resistance. The water vapor permeability of the coated paperboard material (range: 101 ± 43 to 221 ± 13 g·d−1·m−2) was influenced by the hydrophobicity effect of palmitic acid, the non-polar characteristic of activated carbon, and the number of applied layers. The coating formulation selected was a chitosan concentration of 2.0% (w/w), a palmitic acid concentration of 1.8% (w/w), an activated carbon concentration of 1.2% (w/w), and an application of three layers. The coating provides the potential for a paperboard surface application, improving the cellulosic packaging material’s fat and moisture barrier properties and maintaining biodegradability and recyclability.