Juxtacellular interactions play an essential but still not fully understood role in both normal tissue development and tumour invasion. Using proliferating cell fronts as a model system, we explore the effects of cell–cell interactions on the geometry and dynamics of these one-dimensional biological interfaces. We observe two distinct scaling regimes of the steady state roughness of in-vitro propagating Rat1 fibroblast cell fronts, suggesting different hierarchies of interactions at sub-cell lengthscales and at a lengthscale of 2–10 cells. Pharmacological modulation significantly affects the proliferation speed of the cell fronts, and those modulators that promote cell mobility or division also lead to the most rapid evolution of cell front roughness. By comparing our experimental observations to numerical simulations of elastic cell fronts with purely short-range interactions, we demonstrate that the interactions at few-cell lengthscales play a key role. Our methodology provides a simple framework to measure and characterise the biological effects of such interactions, and could be useful in tumour phenotyping.