This paper presents the results of research on the technical–economic optimization of FDM parameters (Lh—layer height and Id—infill density percentage) for the manufacture of tensile and compression samples from recycled materials (r) of PETG (polyethylene terephthalate glycol) and ASA (acrylonitrile styrene acrylate) in the context of the transition to a circular economy. To carry out our technical–economic study, the fundamental principle of value analysis was used, which consists of maximizing the ratio between Vi and Cp, where Vi represents the mechanical characteristic (tensile strength or compressive strength) and Cp represents the production cost. The results of this study showed that, in the case of tensile samples manufactured by recycled PETG (rPETG), the parameter that significantly influences the results of the Vi/Cp ratios is Lh (the height of the layer), while for the samples manufactured additively from recycled ASA (rASA), the parameter that decisively influences the tensile strength is Id (the infill density percentage). In the case of compression samples manufactured by FDM from recycled PETG (rPETG) and recycled ASA (rASA), the parameter that signified influences the results of the Vi/Cp ratios is Id (the infill density percentage). Following the optimization of the FDM parameters, using multiple-response optimization, we identified the optimal parameters for the manufacture of parts by FDM from rPETG and rASA: Lh = 0.20 mm and Id = 100%. The results of this study demonstrated that the use of recycled plastics from PETG and ASA lends itself to a production and consumption model based on a circular economy.