Résumé : The role of the symmetry energy on the internal constitution and the global structure of a cold nonaccreted neutron star is studied using a set of unified equations of state. Based on the nuclear energy-density functional theory, these equations of state provide a thermodynamically consistent treatment of all regions of the star and were calculated using the four different Brussels-Montreal functionals BSk22, BSk24, BSk25 and BSk26. Our predictions are compared to various constraints inferred from astrophysical observations including the recent detection of the gravitational wave signal GW170817 from a binary neutron-star merger.