The use of advanced wound dressings can significantly support the skin healing process by maintaining optimal conditions for tissue regeneration. In this study, foam-like dressings composed of agarose and chitosan, enriched with vitamin C, were developed using a simple and cost-effective freeze-drying method. Three types of chitosan with varying molecular weights (low, medium, high) were used to investigate their impact on the biological, physicochemical, and mechanical properties of the resulting foams. All fabricated biomaterials were biocompatible, non-toxic, and did not promote cell adhesion to their surfaces. The foams exhibited highly porous, hydrophilic microstructures with excellent fluid absorption capacity (~20 mL/g) and sustained vitamin C release over the first 24 h. Chitosan molecular weight had no significant effect on biological properties, but influenced samples’ wettability and mechanical parameters. The hydrophilic character of samples was observed in all tested biomaterials, with the strongest enhancement of hydrophilicity noted for the low molecular weight variant. The highest tensile strength was observed in samples prepared with medium molecular weight chitosan. The results indicate that among the analyzed variants, agarose-chitosan foam biomaterials containing medium molecular weight chitosan exhibited the most favorable properties, making them the most promising candidates for the treatment of wounds with excessive exudate.