The error : 

This operation would create an incorrectly structured document.

The Code : 

        public static void Ecrire_Log(string IP, string UserID, string Guid, string Fonction, string Information)
        {
            XDocument doc = XDocument.Load("C:\\xmllog.xml");

            /*
            CFER_Log log = new CFER_Log() { IP = IP,
                                            UserID = UserID, 
                                            Guid = Guid, 
                                            Fonction = Fonction, 
                                            Information = Information };*/

            XElement XML_log = new XElement("log",
                                   new XElement("IP", IP),
                                   new XElement("UserID", UserID),
                                   new XElement("Guid", Guid),
                                   new XElement("Fonction", Fonction),
                                   new XElement("Information", Information));

            //XElement XML_log = new XElement("logs",IP, UserID, Guid, Fonction, Information);

            doc.AddFirst(XML_log);
            doc.Save("C:\\xmllog.xml");
            //XML_log.Save("c:\\xmllog.xml");
        }

The XML Doc..
<?xml version="1.0" encoding="utf-8"?>
<logs>
	<log>
 	 <IP>127.0.0.1</IP>
	  <UserID>berdav</UserID>
	  <Guid>someguid</Guid>
 	 <Fonction>somefunction</Fonction>
 	 <Information>someaction</Information>
	</log>
</logs>