A method and system improving energy efficiency of a turbojet engine by optimizing rotating speed of a fan and operability of an engine, by freeing the fan from exclusive control of a low-pressure (LP) shaft by providing combined control with a high-pressure (HP) shaft when cruising power has been reached. The turbojet engine include at least one LP turbine and one HP turbine coupled to coaxial LP shafts and HP shafts, respectively, which can drive LP and HP compressors, respectively. The LP compressors include a fan that forms a first primary air-intake compression stage. The LP and HP shafts are mounted on one of two driving mechanisms, an inner ring gear, and a planet carrier for a planetary gear train for driving the fan, the HP shaft being mounted on a disengagement mechanism and the fan being coupled to the planetary gear train via an outer driven ring gear.