A timeline written by Thespitron 6000.
In 1560, France and Scotland were jointly ruled by the married couple of Francis II of France and Mary of Scotland. In December 1560, Francis dies at the age of 16 due to an abscess in the brain caused by an ear infection. Mary went back to Scotland after his death, and Francis's younger brother Charles became Charles IX. The French Wars of Religion happened, as did the Scottish Reformation, with the end result that France remained Catholic with a new Bourbon dynasty on the throne and Scotland joined with England in the Union of the Crowns in 1603.
In this timeline, that didn't happen. Francis's cold, the one that turned into an ear infection and ultimately killed him, didn't progress that far. Instead, he lived another seven years, long enough to father a child with his wife Mary. As a result, the heir to the throne of France is also the heir to the throne of Scotland, resulting in a more personal union between France and Scotland–and, quite possibly, England as well.
So far it has reached 1573, although Thespitron 6000 intends to take it all the way to the present. It can be read here.