A method of making a fiber preform, and the preform, for fabricating a turbine engine blade out of composite material, the method including: making a single-piece fiber blank by three-dimensional weaving with layers of longitudinal yarns interlinked by yarns of layers of transverse yarns; and shaping the fiber blank to obtain a single-piece fiber preform including a portion forming an airfoil preform and at least one portion forming a platform preform. During weaving, yarns of a first group of longitudinal yarns are extracted from the fiber blank beside one of side faces of the blank to form a portion corresponding to a blade platform preform, and yarns of a second group of longitudinal yarns are inserted into the fiber blank with mutual crossing of the yarns of the first group and the yarns of the second group.