A turbomachine blade or vane is made of composite material including fiber reinforcement obtained by three-dimensional weaving of yarns and densified by a matrix. The blade or vane includes a first portion constituting at least an airfoil exhibiting two faces each connecting a leading edge to a trailing edge, the first portion forming a single part with at least one second portion present only on one of the faces of the airfoil, the second portion constituting a portion of at least one of the following elements: a flowpath delimiting outer portion of an inner platform, an inner portion of an inner platform, a flowpath delimiting inner portion of an outer platform, and an outer portion of an outer platform, the portions of the fiber reinforcement corresponding to the first and the second portions of the blade being at least partially mutually imbricated, with yarns of the first portion of the fiber reinforcement penetrating into the second portion of the fiber reinforcement.