Mary was three years older than Henri, and discussions regarding the union of the two royal children grew serious around 1530, while the young prince was being held hostage by Charles V in Spain [subject for a post of its own]. The Peace of Cambrai (1529), which secured the ransom of François's sons, included a clause affirming the French-English marriage. But in October 1530, negotiations with England stalled, for two reasons: François suspected Henry VIII intended to use Henri as security for the debt François owed him, and secondly, questions over Mary's legitimacy were beginning to cloud the issue. Henry VIII was by this time seeking an annulment of his marriage with Mary's mother, Catherine of Aragon, and François feared marrying his son to a bastard. Negotiations did continue until 1532, but once the outcome of Henry VIII's suit became evident, François abandoned the match. Instead, he wed Henri in 1533 to Caterina Maria de Medici, the cousin (often called the niece) of Pope Clement VII.
How would the match between Henri and Mary, had it occurred, have changed history? It's interesting to speculate. It doesn't seem as though it would have derailed Henry VIII from his quest to rid himself of Catherine of Aragon, since he continued with his suit even as he negotiated with France. What is interesting is what would have happened once Henri became Dauphin. At the time of the negotiations, he was only second in line to the French throne. However, his older brother François died in 1536. The couple would eventually have ruled both France and England. This surely would have had great repercussions on the playing out of the religious question in the two countries.
[Source: Henry II, King of France 1547-1559 by Frederic Baumgartner (Duke UP, 1988)]