A bit of a low probability What if, but...
Mary Stuart was the next in line for the English throne after Elisabeth (her son James ended up becoming King of England, of course), and was married to the King of France, Francis II.
Francis II was a sickly, stumpy child, who died of an ear infection (and may have been infertile). But his brother, Charles IX, was healthy enough. So let's presume a sperm zigged when it should have zagged, and Francis II of ATL is a healthy, robust boy. As in OTL, Mary is a brilliant, charming girl, who makes an impression at the French Court, and in 1559 she gives birth to a healthy baby boy, who is named Arthur. The future king of France, and the future king of Scotland.
Now what?