Remember that FUSE ESB is all about flows, you will want to start a flow that will invoke on the CXF BC, if that is the CXF SE then you will want something to invoke on the SE since it typically acts as a consumer on the NMR, the CXF BC can act as either. In your scenario you want to use CXF BC provider to invoke on your Axis based service.
I suppose the question is when do you want to invoke on this? What is the trigger that will send the message to the CXF BC? You may not necessarily want to invoke on this from the CXF SE, for example you might pick the message up from a JMS queue (using a JMS consumer endpoint) that will send it to the CXF BC.
If you want to invoke on it from the CXF SE, you could use the CXF Proxy more info here. The question then would be what starts the CXF SE processing? This comes back to the original question of what event starts the flow?