A fiber preform is made solely from a deformable base fiber structure thats initially in the form of a plane plate constituted by superposed two-dimensional fiber plies bonded together by needling. Cuts and/or splits are formed in the base fiber structure, and the preform is made from the cut and/or split base fiber structure by making use of its ability to be deformed. The structural part is obtained by densifying the preform using a material that constitutes a composite material matrix. It is possible to use a single fiber structure plate which is deformed with the help of splits or cuts so as to obtain the desired preform and in which continuity of the base fiber structure is preserved, or else a plurality of base fiber structure plates can be used which are assembled together by mutual interfitting via the splits or cuts, by deforming at least one of the plates.