This is one of the biggest inaccuracies of The Tudors, the way that they have Henry's two sisters, Margaret and Mary, amalgamated into one woman, Princess Margaret, and instead of Mary marrying King Louis XII Henry sends Margaret to marry the King of Portugal. I really have no idea why Michael Hirst did this as Princess Mary Tudor married Louis XII and had the Boleyn sisters as her ladies. She did not poison him, he died of natural causes.
The timing is out as well, as Mary travelled to France in 1514 to marry Louis on 9th October 1514 so this was many years before the Chateau Vert Masque of 1522 where you see her trying to persuade Henry not to send her to Portugal. Mary was married to Charles Brandon by this time and, yes, she did marry him in France shortly after Louis' death.
The real Margaret Tudor married James IV of Scotland in 1503.
I really hate the way that Hirst mixes these two women into one and completely rewrites history. By having the character of Margaret (who's really Mary) die quite early and before she has a daughter, Frances Brandon, he eliminates Lady Jane Grey, Mary's granddaughter, and by writing out the real Margaret Tudor who goes to Scotland and marries James IV, he eliminates James V, Mary Queen of Scots and James VI/I! Very odd!