I’ve been using Blender for about a week now, absolutely love it and the amazing community behind it, but I am running into a problem I can not solve for the life of me.
Make a plane and subdivide it then deform the plane along the curve. The plane should be long and thin and roughly match the aspect ratio of the image you are going to apply to it. Then unwrap the pane and use UV coordinates to assign the image to the plane. When you add the curve modifier to the plane, the image map will follow.
You could also just model a single frame that looks like your image of a single frame of film. Then use the array modifier followed by a curve modifier to deploy the mesh along the curve. No mapping needed, you would have real geometry.