I will provide an answer to my question.
Even if it work on IE and with specific command on Chrome, this is a security issue set on the server side, only the server can change it by modifing the Access-Control-Allow-Origin
I didn't find a workaround to avoid this CORS problem from the client side. My solution was to move my HTML page on the same domain as my SharePoint. I have now my SharePoint : www.mysharepoint.com
, and my mobile webapp www.mysharepoint.com/mobile/index.html