The disclosed embodiments concern an aircraft fuselage section made of composite material with an internal skeleton having frames that form the radial structure of the fuselage and stringers that form the longitudinal structure of said fuselage, and a skin made of composite material, surrounding the internal skeleton, with said skin having an evolving thickness along a longitudinal axis X, with an approximately constant, regular interior profile. The disclosed embodiments also concern a process for manufacturing the skin of an aircraft fuselage section made of composite material, having a draping operation for strips of fibers precoated with resin around a mold, with the number of strips of fibers varying longitudinally depending on the area of the fuselage being considered so as to create a skin with an evolving thickness.