I assume Wanadoo Livebox is a wireless router. If the router is compatible, it should be detected by the DS automatically. For troubleshooting, you can try entering the IP address, Gateway, and DNS IP's manually in Mario Kart's WiFi config. You can also try enabling the DMZ from your router settings. Be sure to enter your WEP key into Mario Kart if you're using one.
Here's Nintendo's help section
http://www.nintendowifi.com/consumerservice/showCategory.do?catId=Connecting_Home*edit*
Anyone with working wifi want to play?
Code: 330774746736 | Name: Eikon