This fitting for two-way opening windows or French-windows is adapted to be operated by means of a single handle for imparting to the fitting a locked position and two opening positions; the fitting is disposed between the fixed frame and the movable frame of the window and comprises on the one hand at least one locking member rigid with a control rod disposed on one of the frames and adapted to be moved through a distance corresponding to two successive pitches by actuating the handle, and on the other hand at least one keeper engageable by the locking member and disposed on the other frame, this keeper comprising locking means of which one component, the locking member or the keeper, is movable through a distance corresponding to one pitch of the movement performed by the control rod in the direction of travel thereof.