I think you're using a copy constructor for the wrong reason here.
I am a beginner C++ coder...
I can see that. If you want to learn good C++ from the beginning, I can recommend you the C++ book by Sthepen Prata. I read it last summer, and I really learned a lot :-)
...and do not know how to properly call:
MyPicture(const MyPicture& Copy) : Image(Copy.Image), Sprite(Copy.Sprite)
You can't.
The constructor you have takes a object of another "MyPicture"-object as argument. How are you going to create the first object of the class if you have no other constructor?
The point of having a Copy Constructors (or Constructors with Deep Copying) is for copying the data pointers points to, and not the address the pointer is pointing at. And since you're not using any pointers or are allocating any memory you don't need such a constructor.
And what are your class really gonna do?? I mean, isn't it just easier if you'll:
sf::Image img;
img.LoadFromFile("bajs.png");
sf::Sprite spr;
spr.SetImage(img);