ABSTRACT The low dark matter density in the Fornax dwarf galaxy is often interpreted as being due to the presence of a constant density ‘core’, but it could also be explained by the effects of Galactic tides. The latter interpretation has been disfavoured because it is apparently inconsistent with the orbital parameters and star formation history of Fornax. We revisit these arguments with the help of the APOSTLE cosmological hydrodynamics simulations. We show that simulated dwarfs with similar properties to Fornax are able to form stars after infall, so that star formation is not necessarily a good tracer of infall time. We also examine the constraints on the pericentre of Fornax and point out that small pericentres (<50 kpc) are not currently ruled out by the data, allowing for Fornax to be tidally influenced on its current orbit. Furthermore, we find that some dwarfs with large orbital pericentres can be stripped prior to infall due to interactions with more massive galaxies. Tidal effects lead to a reduction in the dark matter density, while the profile remains cuspy. Navarro–Frenk–White profiles are consistent with the kinematic data within 3σ in the innermost regions, while profiles with shallow cusps or cores provide a better fit. We predict that if the reduction of the dark matter density in Fornax occurs, at least in part, because of the action of Galactic tides, then tidal tails should be visible with a surface brightness limit of ∼35–36 mag arcsec−2 over a survey area of ≳100 deg2.