We present the first results of an Atacama Large Millimeter Array survey of the lower fine-structure line of atomic carbon [C I] (P-3(1)-P-3(0)) in far-infrared-selected galaxies on the main sequence at z similar to 1.2 in the COSMOS field. We compare our sample with a comprehensive compilation of data available in the literature for local and high-redshift starbursting systems and quasars. We show that the [C I] (P-3(1) -> P-3(0)) luminosity correlates on global scales with the infrared luminosity LIR, similar to low-J CO transitions. We report a systematic variation of L[C-I](3)p1-(3)p(0)/L-IR as a function of the galaxy type, with the ratio being larger for main-sequence galaxies than for starbursts and submillimeter galaxies at fixed LIR. The L [C-I](3)p1-(3)p(0)/LCO(2-1) and M[(C I])/ M-dust mass ratios are similar for main sequence galaxies and for local and high-redshift starbursts with in a 0.2. dex intrinsic scatter, suggesting that [C-I] is a good tracer of molecular gas mass as CO and dust. We derive a fraction of f([CI]) = M-[C I]/M-C similar to 3%-3% of the total carbon mass in the atomic neutral phase. Moreover, we estimate the neutral atomic carbon abundance, the fundamental ingredient to calibrate [C I] as a gas tracer, by comparing L[C-I](3)p1-(3)p(0) and available gas masses from CO lines and dust emission. We find lower [C I] abundances in main-sequence galaxies than in starbursting systems and submillimeter galaxies as a consequence of the canonical a CO and gas-to-dust conversion factors. This argues against the application to different galaxy populations of a universal standard [C I] abundance derived from highly biased samples.