Do I need to get the window handle (for Windows HWND) from GTK+ to integrate?
Yes. Take a look at other sources (those for Qt, wxWidgets, ...) and try to do the same kind of stuff :lol:
The Qt example might be useful to you, there is some GTK related code in it because Qt is built on top of GTK on Linux.
Qt isn't built on top of GTK on Linux, the only relation is a theme engine for Qt that uses GTK+ drawing code.
I think you can easily integrate SFML with GTK+ using the RenderWindow constructor that accepts the window handle as parameter and by properly redrawing the window at each frame.