You can get the value of "file" property of GtkImage using g_object_get_property. Something on these lines:  
GValue value = {0,}; 
/* If you have glib version 2.30 or higher use:
* GValue value = G_VALUE_INIT;
*/
g_value_init (&value, G_TYPE_STRING);
/* Assuming image is a valid GtkImage */
g_object_get_property(G_OBJECT(image), "file", &value);
printf("\n Filename = %s\n", g_value_get_string(&value));
Side note: To make use of the Glib's type system, g_type_init() should have been called. g_type_init() is called internally as a consequence of Gtk initialization through gtk_init.
Hope this helps!