I'm afraid that's not possible...
Since WPF controls are not Win32 controls behind the scenes (the MS specific HWND or the more general HANDLE), like most WinForms controls are, providing a HANDLE to libvlc for rendering is not possible or not easy.
See here
All WPF elements on the screen are ultimately backed by a HWND. When you create a WPF Window, WPF creates a top-level HWND, and uses an HwndSource to put the Window and its WPF content inside the HWND. The rest of your WPF content in the application shares that singular HWND. An exception is menus, combo box drop downs, and other pop-ups. These elements create their own top-level window, which is why a WPF menu can potentially go past the edge of the window HWND that contains it.
You could try to use a Window and attempt to get its Handle like this:
IntPtr windowHandle = new WindowInteropHelper(windowInstance).Handle
Then pass this handle to libvlc. Remember to obtain this handle no sooner than inside the Loaded event of the window, see here
But this will limit you to using a top level Window control, which doesn't seem to be what you want.