We examine the role of the large-scale galactic-dynamical environment in setting the properties of giant molecular clouds in Milky Way-like galaxies. We perform three high-resolution simulations of Milky Way-like discs with the moving-mesh hydrodynamics code AREPO, yielding a statistical sample of ~80000 giant molecular clouds and ~55000 HI clouds. We account for the self-gravity of the gas, momentum, and thermal energy injection from supernovae and HII regions, mass injection from stellar winds, and the non-equilibrium chemistry of hydrogen, carbon, and oxygen. By varying the external gravitational potential, we probe galactic-dynamical environments spanning an order of magnitude in the orbital angular velocity, gravitational stability, mid-plane pressure, and the gradient of the galactic rotation curve. The simulated molecular clouds are highly overdense (~100x) and overpressured (~25x) relative to the ambient interstellar medium. Their gravoturbulent and star-forming properties are decoupled from the dynamics of the galactic mid-plane, so that the kpc-scale star formation rate surface density is related only to the number of molecular clouds per unit area of the galactic mid-plane. Despite this, the clouds display clear, statistically significant correlations of their rotational properties with the rates of galactic shearing and gravitational free-fall. We find that galactic rotation and gravitational instability can influence their elongation, angular momenta, and tangential velocity dispersions. The lower pressures and densities of the HI clouds allow for a greater range of significant dynamical correlations, mirroring the rotational properties of the molecular clouds, while also displaying a coupling of their gravitational and turbulent properties to the galactic-dynamical environment.