FIREBALL (the Faint Intergalactic Redshifted Emission Balloon, funded by CNES-NASA, PI C.Martin, Caltech) is a balloon-borne 1m telescope coupled to an ultraviolet Multi Object Spectrometer (MOS), designed to study the faint and diffuse emission of the circumgalactic medium. The third flight of the experiment is planned in summer 2017. The goal of this paper is to describe the accurate pointing system of the 5-metres high / 1500kg gondola - that has been designed to fulfill stringent pointing requirements: less than 1 arcsec in elevation and cross elevation, and about 1 arcmin in field rotation (around the line of sight axis), over long integration time (a few hours). The pointing system is based on a multi stage closed loop scheme (4 Degrees Of Freedom), relying on a 1DOF gondola azimuth controller, a 2DOF gimbal frame supporting a 1.2-meter plano siderostat, and a 1DOF field rotation control system. The attitude determination is based on the hybridization of two accurate sensors: a Fiber Optic Gyrometer measurement unit and a star sensor integrated inside the instrument. The manuscript presents the design of the ACS. We also focus on flight train stability issues - due to the pendulum and torsion modes -, on the geometric equations specific to a siderostat pointing system, and on the description of the tests facilities.