A weft insertion system includes at least one rapier provided with weft yarn clamping means for drawing a weft and a reed provided with dents made of a magnetic material, and wherein the rapier has at least one permanent magnet whose direction of polarization extends along a direction which is perpendicular to a longitudinal axis of the reed dents when the reed is in a back position and to a translation direction of the rapier, the at least one permanent magnet exerts an attractive magnetic effort (E, E′) between the rapier and the dents of the reed and the reed has a variable magnetic permeability along its longitudinal axis, and the rapier has a lateral face oriented towards the reed and the at least one permanent magnet has a direction of polarization perpendicular to the direction of travel of the rapier and secant with the lateral face.