I'm not 100% sure I understand your problem, but I think you want the background image to react to the camera movement? If so, maybe try adding a flat plane with the same proportions as the background image. I usually make it a child of the camera and zero out the positions and rotations. Drag it out of the Camera and position it to fill up your screen and add that background image. Now when you move the camera closer, you will also get closer to the image.
Things to keep in mind. Your camera move can't be too dramatic since it's a flat image. Subtle is better here. You may need to move your image farther away from the camera to help control that. You will also have to scale it back up to fill the screen.
I'd probably add a Corona Compositing tag to make sure the background image doesn't block light and cast a shadow.
If you want to learn something really useful, not sure your level of C4D knowledge, learn about Camera Mapping. If you aren't familiar, it's the technique that is used when you only have a flat image or can afford to build a 3D version of the scene, so now you can make small 3D moves and the scene appears 3D. In your case, using simple objects like planes, cylinders and cubes, line them up with your image. I can't remember if you need to cut out the different shapes in Photoshop too. Using the Calibrate Camera, and Projection tag, it can magically transform your background into a 3D scene. Again, works best with smaller camera moves. I found this OLD C4D tutorial that seems pretty clear showing the process.
