(1) Background: Acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent for the coronavirus disease (COVID-19) that has led to a pandemic that began in March 2020. The role of the SARS-CoV-2 components on innate and adaptive immunity is still unknown. We investigated the possible implication of pathogen-associated molecular patterns (PAMPs)–pattern recognition receptors (PRRs) interaction. (2) Methods: We infected Calu-3/MRC-5 multicellular spheroids (MTCSs) with a SARS-CoV-2 clinical strain and evaluated the activation of RNA sensors, transcription factors, and cytokines/interferons (IFN) secretion, by quantitative real-time PCR, immunofluorescence, and ELISA. (3) Results: Our results showed that the SARS-CoV-2 infection of Calu-3/MRC-5 multicellular spheroids induced the activation of the TLR3 and TLR7 RNA sensor pathways. In particular, TLR3 might act via IRF3, producing interleukin (IL)-1α, IL-1β, IL-4, IL-6, and IFN-α and IFN-β, during the first 24 h post-infection. Then, TLR3 activates the NFκB transduction pathway, leading to pro-inflammatory cytokine secretion. Conversely, TLR7 seems to mainly act via NFκB, inducing type 1 IFN, IFN-γ, and IFN-λ3, starting from the 48 h post-infection. (4) Conclusion: We showed that both TLR3 and TLR7 are involved in the control of innate immunity during lung SARS-CoV-2 infection. The activation of TLRs induced pro-inflammatory cytokines, such as IL-1α, IL-1β, IL-4, and IL-6, as well as interferons. TLRs could be a potential target in controlling the infection in the early stages of the disease.