The polymer foil industry is one of the leading producers of plastic waste. The development of new recycling methods for packaging products is one of the biggest demands in today’s engineering. The subject of this research was the melt processing of multilayered PET-based foil waste with PETG copolymer. The resulting blends were intended for additive manufacturing processing using the fused deposition modeling (FDM) method. In order to improve the properties of the developed materials, the blends compounding procedure was conducted with the addition of a reactive chain extender (CE) and elastomeric copolymer used as an impact modifier (IM). The samples were manufactured using the 3D printing technique and, for comparison, using the traditional injection molding method. The obtained samples were subjected to a detailed characterization procedure, including mechanical performance evaluation, thermal analysis, and rheological measurements. This research confirms that PET-based film waste can be successfully used for the production of filament, and for most samples, the FDM printing process can be conducted without any difficulties. Unfortunately, the unmodified blends are characterized by brittleness, which makes it necessary to use an elastomer additive (IM). The presence of a semicrystalline PET phase improves the thermal resistance of the prepared blends; however, an annealing procedure is required for this purpose.