I found this way:
GdkPixmap *backPixMap = gdk_pixmap_create_from_xpm ( window , NULL , NULL , fileName );
gdk_window_set_back_pixmap( GTK_WIDGET( window )->window , backPixMap , FALSE );
but it seems that GdkPixmap is obsolete now...
So, with GTK3, how can I set the background image of a GtkWindow?