The objective of this work was to determine a suitable combination of the polysaccharide mesquite seed gum (MSG) and the protein Nile tilapia fish gelatin in the composite MSG/gelatin film for food packaging applications, and to evaluate the effect of cellulose nanocrystals (CNCs) on the film. MSG and gelatin were extracted from mesquite seeds and Nile tilapia residues, respectively, and the CNCs from mesquite pods by acid hydrolysis. The MSG:gelatin ratio with the best combination of tensile and barrier properties was used to produce the bionanocomposite films, by adding different CNC contents to the MSG/gelatin dispersion. The MSG:gelatin ratio of 1:1 had a good combination of water vapor permeability (WVP) and tensile strength. The properties of the MSG/gelatin films were improved by the CNCs, mainly at 5 wt%, which produced the highest tensile strength and modulus, more than 30% higher than those of the control film, and the lowest WVP, 23% lower than that of the control. Higher CNC contents resulted in the aggregation of nanocrystals, impairing barrier and tensile properties. The nanocomposite film with MSG, gelatin, and CNCs at the respective weight ratios of 1:1:0.1 presents the best overall properties for food packaging applications.