Ok now I have also replaced the html in the module/ ps_searchbar.tpl
<!-- Block search module TOP -->
<div id="_desktop_search_widget">
<div id="search_widget" class="search-widget" data-search-controller-url="{$search_controller_url}">
<form method="get" action="{$search_controller_url}">
<input type="hidden" name="controller" value="search">
<input class="input-search" type="text" name="s" value="" placeholder="Rechercher">
<button type="submit">
<i class="fa fa-search search"></i>
</button>
</form>
</div>
</div>
<!-- /Block search module TOP -->
But the search icon is over the search bar.
Almost there but I cannot find on the CSS where to set that rules to have it on the same line.