A turbofan engine with a nacelle and a flow path, in which the nacelle comprises a movable cowl that makes it possible to define a window between the flow path and the outside, veils with a first edge fixed to the movable cowl and alternately assuming a folded position or a deployed position across the flow path, and a pneumatic system displacing a second edge of the veils from the folded position to the deployed position and vice versa. The pneumatic system comprises a rigid main roll, for each veil, at least one extendable secondary roll fixed to a second edge of the veil, and a pressurization and depressurization system which, alternately, generates a pressure or a depression in each secondary roll. Replacing the reverse doors and their driving mechanisms with flexible veils and a pneumatic system allows for a weight reduction.