That depends on if the Orange livebox uses proprietary protocols to communicate, AND if the BT system supports it. Since Orange is primarily a French system, and of course, BT is British, it would not surprise me if they are totally incompatible. Does BT allow 3rd party modems, or do BT subscribers have to use BT supplied modems? Someone from the UK will have to join in to answer that.

In theory, you should be able to do what you want simply by calling BT and telling them you have a new Modem so they can register the MAC address of that device to your account. But again, if either system or device requires any proprietary protocols, you will be out of luck, and will need to purchase a new BT that meets your needs, or buy a WAP (wireless access point). That said, you might be able to configure the Orange device as a WAP only, and connect it to your BT router as you would another PC, then wirelessly access the Internet via the Orange, through the BT, then out to the world.