A process for shaping, by compaction, a fibrous structure obtained by three-dimensional or multilayer weaving between a plurality of layers of warp yarns and a plurality of layers of weft yarns. The yarns of each plurality of layers of warp yarns and layers of weft yarns are coated with a sizing composition. The shaping includes a pre-compaction stage followed by a stage of final compaction of the fibrous structure. During pre-compaction and final compaction, the fibrous structure is at a temperature greater than or equal to the softening temperature of the sizing composition. The process further includes the cooling of the fibrous preform obtained after final compaction of the fibrous structure.