How to add an autocomplete field with pure javascript
Thanks to Clive for his help ! To active the autocomplete, I should re-attach the autocomplete behavior after added my new element.
nodeSelectorWidget: function (args) {

      // Adding the autocomplete field
      var createField = function() {
        var input = document.createElement('input');

        input.classList.add('form-autocomplete');
        input.setAttribute('data-autocomplete-path', '/fr/autocomplete/custom');

        return input;
      }

      var container = document.createElement('div');
      container.className = 'nodeselector-widget';

      container.appendChild(createField());

      // Re-attach autocomplete behavior to active the autocomplete on the added input
      Drupal.behaviors.autocomplete.attach(container);


      return container;

    }