Following my last post I've been looking at portrait paintings from the Tudor period for signs of red hair. These are the fruits.
Mary Tudor, Queen of France
Mary was the daughter of Henry VII and younger sister of Henry VIII. She married King Louis XII of France. A Venetian ambassador described her as "a paradise - tall, slender, grey-eyed, possessing an extreme pallor." According to Wikipedia she "wore her glorious silken red-gold hair flowing loose to her waist."
Joan of Austria
Joan was the first wife of Grand Duke Francesco de Medici. I couldn't find a mention of her hair colour, but in this painting she looks pretty ginger.