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Glaciers and ice streams flowing over sediment beds commonly have a layer of ice‐rich debris adhered to their base, known as a “frozen fringe,” but its impact on basal friction is unknown. We simulated basal slip over granular beds with a cryogenic ring shear device while ice infiltrated the bed to grow a fringe, and measured the frictional response under different effective stresses and slip speeds. Frictional resistance increased with increasing slip speed until it plateaued at the frictional strength of the till, closely resembling the regularized Coulomb slip law associated with clean ice over deformable beds. We hypothesize that this arises from deformation in a previously unidentified zone of weakly frozen sediments at the fringe's base, which is highly sensitive to temperature and stress gradients. We show how a rheologic model for ice‐rich debris coupled with the thermomechanics of fringe growth can account for the regularized Coulomb behavior.