Advantageously, the shielding device comprises two textile sleeves having separate rest diameters but assembled at one of their annular ends, so that the diameter of the connecting sleeve is adapted to the size of the connector independently of the diameter of the protective sleeve, adapted, for its part, to the elongate elements to be protected. The size of the shielding device is therefore adapted to the connector(s) and to the elongate elements in a differentiated manner along its length, which makes it possible to adjust the weight of the device. In addition, advantageously, the body of the protective sleeve in the extension of its annular front part, has a rest diameter D1 substantially corresponding to diameter in operation. Thus, when this protective sleeve receives elongate elements to be protected, the body is not in the expanded state and maintains its properties of shielding and mechanical protection. The same technical effect can be observed for the connecting sleeve. The diameter of the body of the connecting sleeve in the extension of its annular rear part may be substantially in the order of D2 in operation, or expand to conform to the shape of the connector as described below.

Advantageously, the securing between the rear part of the connecting sleeve and the front part of the protective sleeve is configured so that it is electrically conductive. Electricity is thus conducted from the protective sleeve to the connecting sleeve including through the first securing area, and vice versa.