Formulating pharmaceutical cocrystals as inhalable dosage forms represents a unique niche in effective management of respiratory infections. Favipiravir, a broad-spectrum antiviral drug with potential pharmacological activity against SARS-CoV-2, exhibits a low aqueous solubility. An ultra-high oral dose is essential, causing low patient compliance. This study reports a Quality-by-Design (QbD)-guided development of a carrier-free inhalable dry powder formulation containing a 1:1 favipiravir–theophylline (FAV-THP) cocrystal via spray drying, which may provide an alternative treatment strategy for individuals with concomitant influenza infections and chronic obstructive pulmonary disease/asthma. The cocrystal formation was confirmed by single crystal X-ray diffraction, powder X-ray diffraction, and the construction of a temperature–composition phase diagram. A three-factor, two-level, full factorial design was employed to produce the optimized formulation and study the impact of critical processing parameters on the resulting median mass aerodynamic diameter (MMAD), fine particle fraction (FPF), and crystallinity of the spray-dried FAV-THP cocrystal. In general, a lower solute concentration and feed pump rate resulted in a smaller MMAD with a higher FPF. The optimized formulation (F1) demonstrated an MMAD of 2.93 μm and an FPF of 79.3%, suitable for deep lung delivery with no in vitro cytotoxicity observed in A549 cells.