What would have happened if Mary Queen of Scots had given birth to a daughter by Francis II before he died? Given Salic law she obviously wouldn't have been able to inherit the throne of France, but would she have been allowed to return to Scotland with her mother, given she was heiress presumptive in Scotland, or would she have been made to remain in France?
Welcome to the board
All things considered, I don't think that France would've junketed Salic Law - they didn't for Charles IX's daughter, and the move wasn't even popular when the subject was broached of having Isabel Clara Eugenia succeed. That said, she would possibly be a powerful pawn on the board - she's far more important than Tante Margot, king's daughter opposed to a king's sister, so she'd probably get a match with D. Sebastiao of Portugal instead (if it still comes down to it) if she remains in France.
However, as to her staying in France, two things: Scotland is becoming more Protestant daily, and would not want their little heiress presumptive schooled by the "Jezebel of our age" Catherine de Medicis - so Mary
and baby Margaret (I saw a TL where Mary named her daughter after her grandmother, but Antoinette seems too foreign) are onboard the first ship back. Also, Mary has a
crown in Scotland, much as she loves France, she doesn't there, so, should her marriage ambitions to Charles IX fail, off she pops to Edinburgh. Princess Margaret would go with her.
But, Mary is in a more volatile situation here. OTL, until James VI was born, she had no heir. Here, she does, and like the one biographer put it "a queen who has produced an heir has both done her duty and dispensable". If Mary doesn't do what the Scots' lords like, there's a reasonable chance that they use little Margaret as the stick to keep her in line, perhaps even to the extent of deposing Mary in favor of Queen Margaret II.