Gate-voltage dependent Hall coefficient RH is measured in high-mobility field-effect transistors of solution-crystallized and vapor-deposited 2,7-dioctylbenzothieno[3,2-b]benzothiophene. The value of RH evolves with density of accumulated charge Q, precisely satisfying the free-electron formula RH = 1/Q near room temperature. The result indicates that the intrinsic charge transport inside the grains is band-like in the high-mobility organic-semiconductor thin films that are of significant interest in industry. At lower temperature, even Hall-effect mobility averaged over the whole polycrystalline film decreases due to the presence of carrier-trapping levels at the grain boundaries, while the free-electron-like transport is preserved in the grains. With the separated description of the inter- and intra-grain charge transport, it is demonstrated that the reduction of mobility with decreasing temperature often shown in organic thin-film transistors does not necessarily mean mere hopping transport.