A facility for simplifying the facilities and tools required to assemble a first aircraft fuselage section and a second aircraft fuselage section by the ends thereof, these sections being fragile, large elements. The facility includes a logistics trolley that can be moved on the floor and immobilized in a position to carry the first section, at least one adjustable support installed on the floor at another position that is adjustable with six degrees of freedom, to carry the second section. Each support can be commanded to adjust the position of the second section in relation to the first section, such as to position one end of the second section in geometric conformity with one end of the first section. This arrangement enables all movements to be made directly on the floor, obviating the need to provide lifting machines or overhead traveling cranes within the assembly facility.