A system includes: a stent having a proximal end a support including the stent engaged thereon, having a longitudinal axis and being equipped with a stop against which the proximal end is applied a sheath having a distal end, which can slide relative to the support and stop, between a distal overlap position of the stent and a proximal release position for deploying the stent, and a first inflatable balloon situated between the support and stent, including a distal portion that protrudes past the distal end, on the distal side thereof when the latter is in the distal position, and having, on the distal side, a transverse section larger than or equal to that of the sheath, the distal end situated back from the distal end in the proximal direction, and situated opposite the distal portion, such that the distal portion protrudes partially past the distal end of the sheath.
