Optical emission line diagnostics, which are a common tool for constraining the properties of the interstellar medium (ISM) of galaxies, become progressively inaccessible at higher redshifts for ground-based facilities. Far-infrared (FIR) emission lines, which are redshifted into atmospheric windows that are accessible for ground-based submillimetre facilities, could provide ISM diagnostics alternative to optical emission lines. We investigated FIR line ratios involving CII λ 158 μm, OIII λ 88 μm, OIII λ 52 μm, NII λ 122 μm, and NIII λ 57 μm using synthetic emission lines applied to a high-resolution ( m gas = 883.4 M ⊙ ) cosmological zoom-in simulation, including radiative transfer post-processing with the code K RAMSES-RT at z = 6.5. We find that the CII/NII122 ratio is sensitive to the temperature and density of photodissociation regions. It might therefore be a useful tool for tracing the properties of this gas phase in galaxies. We also find that NII/NIII is a good tracer of the temperature and that OIII52/OIII88 is a good tracer of the gas density of HII regions. Emission line ratios containing the OIII λ 88 μm line are sensitive to high-velocity outflowing gas.