Turbulence in the edge plasma of a tokamak is a key actor in the determination of the confinement properties. The divertor configuration seems to be beneficial for confinement, suggesting an effect on turbulence of the particular magnetic geometry introduced by the X-point. Simulations with the 3D fluid turbulence code TOKAM3X are performed here to evaluate the impact of a diverted configuration on turbulence in the edge plasma, in an isothermal framework. The presence of the X-point is found, locally, to affect both the shape of turbulent structures and the amplitude of fluctuations, in qualitative agreement with recent experimental observations. In particular, a quiescent region is found in the divertor scrape-off layer (SOL), close to the separatrix. Globally, a mild transport barrier spontaneously forms in the closed flux surfaces region near the separatrix, differently from simulations in limiter configuration. The effect of turbulence-driven Reynolds stress on the formation of the barrier is found to be weak by dedicated simulations, while turbulence damping around the X-point seems to globally reduce turbulent transport on the whole flux surface. The magnetic shear is thus pointed out as a possible element that contributes to the formation of edge transport barriers.