Infections in nonhealing wounds remain one of the major challenges. Recently, nanomedicine approach seems a valid option to overcome the antibiotic resistance mechanisms. The aim of this study was the development of three types of polysaccharide-based scaffolds (chitosan-based (CH), chitosan/chondroitin sulfate-based (CH/CS), chitosan/hyaluronic acid-based (CH/HA)), as dermal substitutes, to be loaded with norfloxacin, intended for the treatment of infected wounds. The scaffolds have been loaded with norfloxacin as a free drug (N scaffolds) or in montmorillonite nanocomposite (H—hybrid-scaffolds). Chitosan/glycosaminoglycan (chondroitin sulfate or hyaluronic acid) scaffolds were prepared by means of electrospinning with a simple, one-step process. The scaffolds were characterized by 500 nm diameter fibers with homogeneous structures when norfloxacin was loaded as a free drug. On the contrary, the presence of nanocomposite caused a certain degree of surface roughness, with fibers having 1000 nm diameters. The presence of norfloxacin–montmorillonite nanocomposite (1%) caused higher deformability (90–120%) and lower elasticity (5–10 mN/cm2), decreasing the mechanical resistance of the systems. All the scaffolds were proven to be degraded via lysozyme (this should ensure scaffold resorption) and this sustained the drug release (from 50% to 100% in 3 days, depending on system composition), especially when the drug was loaded in the scaffolds as a nanocomposite. Moreover, the scaffolds were able to decrease the bioburden at least 100-fold, proving that drug loading in the scaffolds did not impair the antimicrobial activity of norfloxacin. Chondroitin sulfate and montmorillonite in the scaffolds are proven to possess a synergic performance, enhancing the fibroblast proliferation without impairing norfloxacin’s antimicrobial properties. The scaffold based on chondroitin sulfate, containing 1% norfloxacin in the nanocomposite, demonstrated adequate stiffness to sustain fibroblast proliferation and the capability to sustain antimicrobial properties to prevent/treat nonhealing wound infection during the healing process.