This question has been answered by achterbahn. See the first response.
<a href="#" class="search-top" data-toggle="modal" data-focus="true" data-target=".search-modal"><span class="glyphicon glyphicon-search" aria-hidden="true"></span></a>
<!-- Site Search -->
<div class="modal fade search-modal Fixed" role="dialog">
<div class="modal-dialog" role="document">
<div class="modal-content">
<div class="modal-body">
[[!SimpleSearchForm? &landing=`ID de ressource pour les résultats` &tpl=`SiSeaForm`]]
</div><!-- /.modal-content -->
</div>
</div><!-- /.modal-dialog -->
</div><!-- /.modal --><form class="sisea-search-form form-inline" action="[[~[[+landing:default=`[[*id]]`]]]]" method="[[+method:default=`get`]]"> <div class="form-group"> <input type="text" class="form-control" placeholder="Recherche..." name="[[+searchIndex]]" id="[[+searchIndex]]" value="[[+searchValue]]"> <button type="submit" class="btn btn-default" style="margin-top: 0;">Recherche</button> </div><!-- /input-group --> <input type="hidden" name="id" value="[[+landing:default=[[*id]]]]" /> </form>
[[!SimpleSearch? &toPlaceholder=`sisea.results` ]] [[+sisea.results]]