The leaders appeared downright chummy during a joint press conference on Thursday in Paris, mostly skipping by their political differences and focusing on shared priorities like Syria, terrorism and what Macron described as "free and fair trade."

They even exchanged a brief, low-impact handshake after Macron's opening statement, a symbolic counterpoint to their now famous arm-wrestling match in Brussels six weeks ago.

"Thank you for the tour of some of the most incredible buildings anywhere in the world," Trump said as he began his own remarks. "It was a very, very beautiful thing to see."

When asked about Trump's decision to pull the US out of the Paris climate deal, Macron soberly reiterated his own position, but didn't press or attempt to publicly shame his counterpart. The schism on that issue would "absolutely not" prevent France and the US from working together on other matters, he assured, turning kindly in his Trump's direction.

Trump was clearly charmed, echoing Macron's declaration of "friendship" before enthusing at the prospect of a shared dinner later on at the Eiffel Tower. Of the climate deal, he offered: "Something could happen with respect to the Paris accord, we'll see what happens. But we will talk about that over the coming period of time and if it happens, that would be wonderful and if it doesn't that will be OK too."

Trump walks back his past comments criticizing Paris, calling it "one of the most beautiful cities in the world" https://t.co/lrC9zGdrzL — CNN Politics (@CNNPolitics) July 13, 2017

Perhaps it was all a bit of stagecraft. No one expects Trump to seriously reconsider his position on the climate pact. More instructive here were Macron's machinations. In a country where leaders prove themselves in their dealings with Europe, the new president stands to gain influence at home if he proves capable of influencing Trump where others, like German Chancellor Angela Merkel, could not.

The prospect is less of a stretch than it might seem on paper.

Macron entered office this year under ostensibly different circumstances than Trump. But like the President, he pitched voters on a demolition of the status quo and a French take on Trump's promise to "drain the swamp." Macron also upended the traditional partisan hierarchy in France. Though he served as a minister in his predecessor's French Socialist government, he rules now under the banner of his own centrist party, "En Marche!" Trump, though he came to power as a Republican and governs alongside them, sold himself as a right-wing populist. The fiscal conservatism championed by Republicans like House Speaker Paul Ryan was, at least during the campaign, very much an afterthought.

The nationalist and the globalist

The parallels and similarities have some fairly strict limits. Trump is a nationalist. Macron is a proud globalist who came to power by routing the far-right nationalist Marine Le Pen. Trump prefers bilateral diplomacy. He cheered Brexit. He wants to share a private dinner, not a microphone with dozens of world leaders. Macron believes in a robust European Union and has been among the President's foremost critics on climate change policy. Temperamentally, they are also opposites. The handshake drama is resonant, to a point, because it provides a neat example of their respective preoccupations with personal power dynamics.

"My handshake with (Trump), it's not innocent," Macron told the Journal du Dimanche after what appeared to be an introductory arm-wrestling match in Brussels. "It's not the alpha and the omega of politics, but a moment of truth."

In the weeks that followed, Macron has shown himself to be an unusually unpredictable character. His public pronouncements, some of them years old but only recently vaulted into the headlines, have provoked confusion and anger among American liberals, many of whom initially pointed to his victory over Le Pen as a blueprint for Democrats looking to regain power in the US.

The Putin question

But unlike Trump, who has repeatedly expressed doubts over Russia's meddling in the 2016 US election, Macron has been less circumspect on the question. He earned applause among Democrats when he skewered Russian state-owned media during a joint press conference with Vladimir Putin.

"Russia Today and Sputnik were influencers in this campaign who, in several instances, disseminated lies about myself and my campaign," he said as a stone-faced Putin looked on silently. "All of the journalists, including Russian ones, had access to my campaign. ... And that is why it was serious matter that foreign press organizations, under whose influence I don't know, have interfered by publishing serious, untrue accusations in the middle of a democratic campaign."

Contrast that with Trump's own meeting with Putin, after which where was no press conference. What exactly was said between Trump and Putin when the American president "pressed" the Russian one on the issue of election meddling, remains the subject of debate between their two camps.

Macron's observations

But over the past six weeks, Macron has made waves with a handful of less easily categorized remarks and public observations.

In an address to parliament 10 days ago, he shared plans to bypass lawmakers -- whose ranks he suggesting cutting by a third -- if they slowed or opposed his agenda.

"I want all these deep reforms that our institutions seriously need to be done within a year," he said. "These reforms will go to parliament but, if necessary, I will put them to voters in a referendum."

Those comments, and Macron's tweaks to what top White House adviser Steve Bannon might call the "administrative state" didn't go unnoticed by the President's team. Turning to his French counterpart with a smile on Thursday, Trump cheered Macron's "courageous call for that less bureaucracy. It's a good chant, less bureaucracy. We can use it too."

Macron offered his July 3 remarks at the Palace of Versailles, the 17th century home of the "Sun King," Louis XIV. While past French leaders have used the venue in times of crisis, Macron chose it as a backdrop -- ominously so, critics said -- for what amounted to a policy speech.

Jean-Luc Mélenchon, who ran in the first round of the French election as the candidate of the far-left, called Macron's preference for the palace a "sign of the pharaonic drift of this monarchical presidency." Trump has heard similar criticism from his opponents, mostly Democrats, who accuse him of pursuing authoritarian power grabs with executive actions like the travel ban.

Both presidents have also sought to distance themselves, though by very different means, from the political press. For Macron, that means establishing a "Jupiterian" presidency , in which he communicates to the country on his own terms and operates at a remove from the daily politics.

And while that might seem at odds with Trump and his hyperactive social media presence, the leaders seem to share a low opinion of the news media covering their administrations.

Explaining earlier this month why Macron had canceled a traditional Bastille Day press conference, an Elysee source said told the French newspaper Le Monde that his "complex thought process" risked baffling reporters.

Trump could only be impressed.