Interferometric effects between two counter-propagating beams incident on an optical system can lead to a coherent modulation of the absorption of the total electromagnetic radiation with 100% efficiency even in deeply subwavelength structures. Coherent perfect absorption (CPA) rises from a resonant solution of the scattering matrix and often requires engineered optical properties. For instance, thin film CPA benefits from complex nanostructures with suitable resonance, albeit at a loss of operational bandwidth. In this work, we theoretically and experimentally demonstrate a broadband CPA based on light-with-light modulation in epsilon-near-zero (ENZ) subwavelength films. We show that unpatterned ENZ films with different thicknesses exhibit broadband CPA with a near-unity maximum value located at the ENZ wavelength. By using Kerr optical nonlinearities, we dynamically tune the visibility and peak wavelength of the total energy modulation. Our results based on homogeneous thick ENZ media open a route towards on-chip devices that require efficient light absorption and dynamical tunability.