Hi ,
only a CC3 Avatar can be exported from CC3 as FBX.
CC3 Avatars do not have a bone based facial rig which is why you get only the facial morphs as blend shapes/pose morphs in C4D
Just as I get in Blender from CC3.
If you need a facial rig that can be tracked with your facial mocap system in C4D, you will have to build a custom one in C4D.