If Francis II and Mary have a posthumous daughter, then who would be her guardian? I would think it would be one of the "Four Marys" who were Queen Mary's ladies in waiting.
Catherine de Medici threw Mary out of France more or less following Francis II's death, and I'm not sure how the Queen Mother of France would feel about the infant produced by her late son and daughter-in-law. I think the child would stay in France, being a French royal princess after all.
If the daugher survives (and of couse she will in any scenario because its no fun if he doesn't) then she continues to be Queen of Scotland, but without any real ability to rule. With the Treaty of Edinburgh the ascendent Protestants have cut ties with France, despite the fact that their infant Queen is being brought up in that country. So, I would propose that Scotland continue in its state of relative anarchy, with the overthrow and death of Mary of Guise and the fictional rule of an infant Queen.
I think the birth of a posthumous daughter would result in the overthrow of the senior Stewart line. I think James Hamilton might be able to get English support in launching a coup. The Scots did not want to be ruled by either France or England, and with an infant Queen in the power of the French, it is clear that Scotland now needs a King. James Hamilton is the closest to the throne, although there is the possbility that James Stewart, Mary's bastard half-brother, could launch a bid. James seems like he was a good governor, crushing those who opposed Mary in the beginning of her reign and then crushing Mary's forces after her abdictation. I think James Stewart could probably get English support as well, since his succession to the throne would end the possibility of using Scotland as a launch-pad for a claim on the English throne.
I think one definite result of this POD is that the Stuarts (or Stewarts, since Mary's spelling might not ever come into common usage) never succeed to the English throne. In that case, the descendents of Charles Brandon and Mary Tudor are going to inherit. If that is the case and all marriages end up being the same, then
Anne Stanley will become the next Queen of England upon Elizabeth I's death.