Very very faint
Margaret Beaufort, Henry VII's mother was a great great grand daughter of Edward III and that was illegitimate since via John of Gaunt's mistress
http://englishhistory.net/tudor/genealogy.html
Henry VI was the great grandson of Edward III also via John of Gaunt but through his first wife
You'll have to tell me what relation that is!
As I recall the king of France had a better claim to the throne than Henry VII - he effectively conquered England but history is written by the winner and he was smart enough to marry Edward IV's daughter making Henry VIII's claim much more solid