The influenza virus transcribes and replicates its genome inside the nucleus of infected cells. Both activities are performed by the viral RNA-dependent RNA polymerase that is composed of the three subunits PA, PB1, and PB2, and recent studies have shown that it requires host cell factors to transcribe and replicate the viral genome. To identify these cellular partners, we generated a comprehensive physical interaction map between each polymerase subunit and the host cellular proteome. A total of 109 human interactors were identified by yeast two-hybrid screens, whereas 90 were retrieved by literature mining. We built the FluPol interactome network composed of the influenza virus polymerase (PA, PB1, and PB2) and the nucleoprotein NP and 234 human proteins that are connected through 279 viral-cellular protein interactions. Analysis of this interactome map revealed enriched cellular functions associated with the influenza virus polymerase, including host factors involved in RNA polymerase II-dependent transcription and mRNA processing. We confirmed that eight influenza virus polymerase-interacting proteins are required for virus replication and transcriptional activity of the viral polymerase. These are involved in cellular transcription (C14orf166, COPS5, MNAT1, NMI, and POLR2A), translation (EIF3S6IP), nuclear transport (NUP54), and DNA repair (FANCG). Conversely, we identified PRKRA, which acts as an inhibitor of the viral polymerase transcriptional activity and thus is required for the cellular antiviral response.