We determine the inner density profiles of massive galaxy clusters (M200 > 5 × 1014 M☉) in the Cluster-EAGLE (C-EAGLE) hydrodynamic simulations, and investigate whether the dark matter density profiles can be correctly estimated from a combination of mock stellar kinematical and gravitational lensing data. From fitting mock stellar kinematics and lensing data generated from the simulations, we find that the inner density slopes of both the total and the dark matter mass distributions can be inferred reasonably well. We compare the density slopes of C-EAGLE clusters with those derived by Newman et al. for seven massive galaxy clusters in the local Universe. We find that the asymptotic best-fitting inner slopes of 'generalized' Navarro─Frenk─White (gNFW) profiles, γgNFW, of the dark matter haloes of the C-EAGLE clusters are significantly steeper than those inferred by Newman et al. However, the mean mass-weighted dark matter density slopes of the simulated clusters are in good agreement with the Newman et al. estimates. We also find that the estimate of γgNFW is very sensitive to the constraints from weak lensing measurements in the outer parts of the cluster and a bias can lead to an underestimate of γgNFW.