Polysaccharides and proteins are the primary components of edible films used for food packaging. Adding plasticizers such as glycerol or sorbitol during manufacturing can help enhance the properties of films derived from biopolymer combinations. In this study, we aimed to produce sodium alginate/gum arabic/gluten edible films and evaluate the effects of various concentrations of glycerol and sorbitol used as plasticizers on the films’ physical, mechanical, barrier, and optical properties. Using solvent casting, an edible film based on sodium alginate/gum arabic/gluten was plasticized with either glycerol or sorbitol at concentrations of 2, 4, and 6% (w/v). The properties of the edible films were then characterized. Decreases in solubility, tensile strength, and water vapor transmission rate were observed when higher glycerol and sorbitol concentrations were added. The films plasticized with 6% glycerol and 6% sorbitol had the lowest solubility, tensile strength, and water vapor transmission rates. In addition, the films plasticized with glycerol, regardless of concentration, had lower transparency values than those plasticized with sorbitol. The addition of glycerol and sorbitol had insignificant effects on the thickness properties and L values of the films. The absorption peaks of the Fourier-transform infrared spectra patterns of the films plasticized with sorbitol and glycerol were similar, confirming there was an interaction between the plasticizers and polymers. Together, the results demonstrate that sorbitol and glycerol are compatible with sodium alginate/gum arabic/gluten film-forming solutions, indicating that the films obtained could be employed for food packaging.