Electrokinetic effects offer a method of choice to control flows in micro- and nanofluidic systems. While a rather clear picture of these phenomena exists now for the liquid-solid interfaces, the case of liquid-air interfaces remains largely unexplored. Here, we investigate at the molecular level electrokinetic transport in a liquid film covered with ionic surfactants. We find that the ζ potential, quantifying the amplitude of electrokinetic effects, depends on the surfactant coverage in an unexpected way. First, it increases upon lowering surfactant coverage from saturation. Second, it does not vanish in the limit of low coverage but instead approaches a finite value. This behavior is rationalized by taking into account the key role of interfacial hydrodynamics, together with an ion-binding mechanism. We point out implications of these results for the strongly debated measurements of the ζ potential at free interfaces and for electrokinetic transport in liquid foams.