Your simpleviewer.load() line has too many Embed Code Parameters.
Change:

simpleviewer.load("sv-container", "950", "570", "FFFFFF", true, flashvars, null, null, null, false);

... to:

simpleviewer.load("sv-container", "950", "570", "FFFFFF", true, flashvars, null, null, false);

Your gallery is actually embedded correctly but displays white crosses (where images should be) on a white background so you cannot see the problem.
The problem is that the imageURLs and thumbURLs in your gallery's XML file are defined using relative paths and they should be relative to the web page containing the embedding code but they are currently relative to the XML file.
As you have uploaded your complete gallery folder to your web server, then, rather than change all the paths in the XML file, you can simply use a baseURL rather than a galleryURL by changing the line:

flashvars.galleryURL = "http://www.brs-photographiste.com/simpleviewer_cosmetique/gallery.xml"; 

... to:

flashvars.baseURL= "http://www.brs-photographiste.com/simpleviewer_cosmetique/"; 

For reference, the baseURL method of embedding is documented here.

Finally, it works.

With the modifications that you gave me, I have rewrite the code:

<!--START SIMPLEVIEWER EMBED.-->
<script type="text/javascript" src="http://www.brs-photographiste.com/simpleviewer_cosmetique/svcore/js/simpleviewer.js"></script>
<script type="text/javascript">
var flashvars = {};
flashvars.baseURL = "http://www.brs-photographiste.com/simpl … osmetique/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container", "950", "570", "FFFFFF", true, flashvars);
});
</script>
<div id="sv-container"></div>
<!-- END SIMPLEVIEWER EMBED -->

And the gallery displays.
I have no necessary equipment for verified if that works on the mobile devices.

Thank you for your assistant.