Leaking windows can cause wood blackening problems on varnished window sills. To solve this problem, you must first remove the old varnish, clean with oxalic acid, and sand to restore the wood's original color. 

To avoid having to redo this work every two or three years, it is recommended to apply several coats of finishing oil. The oil will provide better protection while allowing the wood to breathe, which can prevent blackening caused by water infiltration under the varnish.