Porous carbon films, attributed to their superior thermal and chemical robustness, are attractive for a number of applications. In the context of molecular separation, a major focus has been on films where the effective pore diameter is lower than 1 nm, e.g., carbon molecular sieves. Only a handful of reports are available on carbon films hosting 2-3 nm size pore channels where gas transport mainly takes place by Knudsen diffusion in contrast to activated transport. Recently, we reported nanoporous carbon (NPC) films, by the pyrolysis of phase-separated blockcopolymer/turanose films, as a gas-permeable mechanical reinforcement for crack-free synthesis of single-layer graphene membranes. However, a dedicated study on the nanostructure and transport properties of the standalone NPC film has been missing. Herein, we show that the NPC film has a perforated lamellar (PL) nanostructure where molecular transport is limited by an interlamellar spacing of similar to 2 nm. The unique PL nanostructure of the NPC film originates from its precursor, i.e., a block-copolymer stabilized by hydrogen bonding with a carbohydrate additive, where the latter also acts as the main carbon-forming agent. This nanostructure is highly sensitive to the carbohydrate/block-copolymer ratio and gives way to a lacey structure below a ratio of 2:1. The transport of gases through the interlamellar spacing takes place predominantly in the Knudsen regime, determined by their molecular mass. Attributed to a thickness of 100 nm, the film yields extremely rapid gas transport with a H-2 permeance over two million gas permeation units (GPU) and H-2/CO2 selectivity over 4.5 in a temperature range of 25-300 degrees C. These properties make the NPC film a promising membrane support and a good choice for the mechanical reinforcement for high-permeance twodimensional membranes for gas separation.