We present a comprehensive suite of high-resolution (parsec-scale), idealised (noncosmological) galaxy merger simulations (24 runs, stellar mass ratio ∼2.5:1) to investigate the connection between interaction-induced star formation and the evolution of the interstellar medium (ISM) in various temperature-density regimes. We use the GIZMO code and the second version of the "Feedback in Realistic Environments" model (FIRE-2), which captures the multi-phase structure of the ISM. Our simulations are designed to represent galaxy mergers in the local Universe. In this work, we focus on the 'galaxy-pair period' between first and second pericentric passage. We split the ISM into four regimes: hot, warm, cool and cold-dense, motivated by the hot, ionised, atomic and molecular gas phases observed in real galaxies. We find that, on average, interactions enhance the star formation rate of the pair (∼30%, merger-suite sample average) and elevate their cold-dense gas content (∼18%). This is accompanied by a decrease in warm gas (∼11%), a negligible change in cool gas (∼4% increase), and a substantial increase in hot gas (∼400%). The amount of cold-dense gas with densities above 1000 cm −3 (the cold ultra-dense regime) is elevated significantly (∼240%), but only accounts for ∼0.15% (on average) of the cold-dense gas budget.