We utilize first-principles theory to investigate the role of electron-phonon interactions within a dataset of monolayer materials. Using density functional theory to describe excited-state transitions and the special displacement method to describe the role of phonons, we analyze the relationship between simple physical observables and electron-phonon coupling strength. For over 100 materials, we compute the band gap renormalization due to zero-point vibrational (ZPR) motion as a measure of electron-phonon interactions and train a machine learning model based on physical parameters. We demonstrate that the strength of electron-phonon interactions is highly dependent on the band gap, dielectric constant, and degree of ionicity, all of which can be physically justified. We then apply this model to 1302 2D materials, predicting the ZPR, which for five randomly selected materials tested agree well with the first-principles predictions. This work provides an approach for quantitatively predicting the ZPR as a measure of electron-phonon interactions in 2D materials.