Can I combine a freelook Camera and a framing transpose?

I was wondering if there was a way to combine the way the camera moves when the mouse moves of a freelook camera with the way the camera moves when a character moves of the framing transpose. I want the mouse to change the angle but I don't want the player moving to change the angle.

I'm trying to make a 3D game and I currently have it set up so that moving forward is in the direction the camera is facing and moving left/right is perpendicular to the direction the camera is looking. The problem is that when I just hold down the move left button without moving the camera the character moves in a circle around the camera instead of in a straight line with the camera following them. Is there another way to do this?

 

Thank you for your response! The aiming rig sounds like what I want but unfortunately I can't find where the sample scenes are. The two places I checked were the options when I create a new scene in an existing project (though I believe those are templates rather than sample scenes) and then the scenes menu when I make a new project but neither place had what you mentioned.

Sorry! I haven't used Unity much.

 

Thank you so much for your help!