Why similar domestic political dynamics produced such different effects is very much a question of electoral mechanics. Under America’s Electoral College system, Donald Trump could beat a candidate who won the popular vote by a majority of three million, while France’s two-round system never gave Ms. Le Pen a chance. It opened the way to Mr. Macron’s victory, which was confirmed six weeks later by a resounding majority in parliamentary elections. Mr. Trump’s erratic debut at the White House, coupled with the shock of the Brexit referendum, also made French voters think twice before taking the nationalist direction.

So here we are, on both sides of the Atlantic, governed by two unique specimens, born of electoral upsets, disrupters of exhausted political systems enjoying large constitutional presidential powers. The two men may pretend to enjoy a warm relationship. They may even think they do, based on their common imperative of fighting terrorism. Yet the way they exercise power and the policies they promote keeps them apart.

Mr. Trump, who campaigned as a populist and rules as one, is accused of diminishing the American presidency. His compulsive tweeting habits, betraying a limited vocabulary, aim to bypass the mainstream media that he loathes; he watches TV, doesn’t read books, takes a lot of time off.

Mr. Macron, as soon as he was elected, reverted to a quasi-monarchical presidential role. His goal, he explained, was to restore authority and dignity to an office that had been weakened by his predecessors Nicolas Sarkozy and Mr. Hollande. His Twitter line is kept strictly to official announcements. He communicates through 90-minute speeches and lengthy interviews studded with references to philosophers, archaic words and refined grammar. He doesn’t think much of French journalists; he would obviously rather control them if he could, instead of just attacking them as “failing.” He is a true workaholic and makes it known that his nights are short.

The two leaders do have a few things in common. They are both lucky — and in politics, luck matters. The American president enjoys buoyant economic conditions, part of a global economic surge; similarly, his French counterpart has benefited from an upswing in the eurozone. They both managed to pass, in their first year, a tax reform criticized by their opponents for mostly benefiting the wealthy and intended to convince the corporate world that they are on its side. But neither conforms to a classic ideological line; pundits in their respective countries struggle to define Macronism or Trumpism.

Still, there is one glaring difference: The approval ratings of President Macron, unlike those of President Trump, are on the rise. Polling experts in France say their president, having realized that it would be difficult to regain voters’ confidence on the domestic scene at this early stage of his reforms, has been trying to win it through principled stances and activism on the world scene. In the United States, polling experts note that despite a booming economy, President Trump struggles to raise his approval ratings from levels lower than those of any of his predecessors in their first year in office.

It is still early in their terms. Keep watching this competition. Much of the future of the liberal democratic West will depend on these two mavericks’ fortunes.