A fiber preform for a hollow turbine engine vane, the preform comprising: a first fiber structure obtained by three-dimensional weaving and comprising at least one main longitudinal portion suitable essentially for forming a pressure side wall of an airfoil; a second fiber structure obtained by three-dimensional weaving and comprising at least one main longitudinal portion suitable essentially for forming a suction side wall of the airfoil; wherein each of the first and second fiber structures (41, 42) further includes a first interlinking zone extending along the front edge of its main longitudinal portion (46, 47), which first zones are integral with each other and form a first interlinking portion of the preform, and a second interlinking zone extending along the rear edge of its main longitudinal portion (46, 47), the second zones being integral with each other and forming a second interlinking portion of the preform; and wherein the main longitudinal portions (46, 47) of the first and second fiber structures (41, 42) are dissociated so as to leave a gap between said main longitudinal portions suitable for forming an airfoil hollow; wherein the first interlinking zones of the first and second fiber structures (41, 42) are woven jointly in interlinked manner and/or the second interlinking zones of the first and second fiber structures (41, 42) are woven jointly in interlinked manner; wherein the main longitudinal portions of the first and second fiber structures (41, 42) are woven jointly in non-interlinked manner, wherein at least one of the fiber structures further includes at least one radial portion (52, 53) extending from the bottom or top edge of its main longitudinal portion and suitable for forming a platform (22, 23) or a fastener flange, characterized in that at least one of the radial portions (52,53) includes an overlap portion (52m, 52v, 53m, 53v) that, when the fiber structure is flat, lies in front of at least a portion of the first interlinking zone of said fiber structure or behind at least a portion of the second interlinking zone of said fiber structure, a gap being left between said overlap portion (52m, 52v, 53m, 53v) and the interlinking zone (43, 44) in question. a first fiber structure obtained by three-dimensional weaving and comprising at least one main longitudinal portion suitable essentially for forming a pressure side wall of an airfoil; a second fiber structure obtained by three-dimensional weaving and comprising at least one main longitudinal portion suitable essentially for forming a suction side wall of the airfoil; wherein each of the first and second fiber structures (41, 42) further includes a first interlinking zone extending along the front edge of its main longitudinal portion (46, 47), which first zones are integral with each other and form a first interlinking portion of the preform, and a second interlinking zone extending along the rear edge of its main longitudinal portion (46, 47), the second zones being integral with each other and forming a second interlinking portion of the preform; and wherein the main longitudinal portions (46, 47) of the first and second fiber structures (41, 42) are dissociated so as to leave a gap between said main longitudinal portions suitable for forming an airfoil hollow; wherein the first interlinking zones of the first and second fiber structures (41, 42) are woven jointly in interlinked manner and/or the second interlinking zones of the first and second fiber structures (41, 42) are woven jointly in interlinked manner; wherein the main longitudinal portions of the first and second fiber structures (41, 42) are woven jointly in non-interlinked manner, wherein at least one of the fiber structures further includes at least one radial portion (52, 53) extending from the bottom or top edge of its main longitudinal portion and suitable for forming a platform (22, 23) or a fastener flange,