Impregnation of a fibrous material made from continuous fibres with a thermoplastic polymer matrix, the fibrous material comprising a thermoplastic sizing polymer and, before impregnation, an initial width. The method comprises an expansion step which is carried out by means of at least two tensioning members (E) and a heating system SC for heating the tensioning members and/or the fibrous material, the expansion being from 1.5 to 5 times the initial width. The expanded fibrous material is cooled below the Tg of the thermoplastic sizing polymer by means of a cooling system before being brought into contact with the thermoplastic polymer matrix.