The utilization of hydrogen gas (H2) as an energy resource is a critical alternative to relieve the current greenhouse effect exacerbated by the excessive use of fossil fuels. The production of pure H2 is usually achieved by its separation from H2/CH4 and H2/CO2 mixtures; however, such process still represents a great challenge due to the inevitable contamination that occurs after the membrane sieving. Here, we investigate the ability of a 2-dimensional material, a nanoporous fluorinated graphene (F-GRA), to perform the separation of H2/CH4 and H2/CO2 using molecular dynamics simulations. We generated three representative nanopores with different morphologies in F-GRA sheets to separately explore their sieving performances for the H2 separation in the H2/CH4 and H2/CO2 mixtures. Our results revealed that the three F-GRA pores have an excellent performance for the H2/CH4 separation, displaying a high permeance for H2 (over 104 GPU) and a complete rejection for CH4; these results suggest an ideal permeability and selectivity for these 2D systems. Additionally, two F-GRA pores, namely, pore2 and pore3, also displayed high separation performance in the case of the H2/CO2 mixture, while the remaining pore, namely, pore1, exhibit poor performance due to the tight obstruction of the CO2 gas inside the nanopore. Combined, our findings exploit the utilization of the nanoporous F-GRA 2D material for the separation of H2/CH4 and H2/CO2 gas mixtures, which might open new possibilities for the future of gas sieving membrane preparation.