(CNN) President Donald Trump deployed the full trappings of formal state entertaining for the first time on Monday in the hopes an elaborate display of diplomacy can lead to a deeper bond with French President Emmanuel Macron.

But beneath the pomp and circumstance the state visit brings -- streets lined with fluttering French and American flags, an elaborate military welcome and a meticulously planned state dinner -- the two leaders are expected to tackle a slew of pressing foreign policy issues, from the Iran deal to the Syrian civil war, counterterrorism and Russian aggression. The daylight between the men on some of those issues will become apparent.

Macron touched down in Washington midday aboard a French government plane. After arriving to Blair House, the presidential guest quarters, he and his wife, Brigitte, strolled to the Lincoln Memorial, surrounded by security agents and journalists.

Later, the couple greeted Trump at the West Wing with kisses on each cheek to formally begin the visit. Joined by Melania Trump, the foursome used golden shovels to plant a European Sessile oak tree on the South Lawn that had been plucked from the Belleau Woods, northeast of Paris, where 9,000 American troops lost their lives during World War I. They departed soon after aboard a helicopter to Mount Vernon, the riverfront estate of George Washington , for a private dinnerof lemon-ricotta agnolotti with citrus butter, salad, ballotine of Dover sole with lemon curd and heirloom asparagus, and chocolate soufflé with cherry vanilla ice cream.

Tweeting on Monday afternoon, Emmanuel Macron previewed his message to Trump.

"The United States and France share a long history, we have led revolutions together to defend freedom and democracy," he wrote. "It is our turn to live up to the example set by our history."

The two leaders get to business on Tuesday following a military welcome on the South Lawn. In the wake of the US-French strikes in Syria, questions remain about Trump's willingness to maintain a military presence in Syria as Macron has urged his US counterpart to do. Trump's harsh new new trade approach has led to fears of a trade war. And a fast-approaching deadline on the Iran deal also looms large.

Macron as Trump whisperer?

Trump has threatened to pull out of the Iran deal and snapback US sanctions on Iran by May 12 unless major changes are made to the agreement brokered by the previous US administration, which capped Iran's nuclear program in exchange for relief from economic sanctions. France, Germany and the United Kingdom -- key signatories to the deal -- are in the midst of negotiations with the US aimed at assuaging some of Trump's concerns, but large gaps still remain.

Already, some US administration officials have been preparing options for withdrawal from the agreement, hoping to be ready should Trump abruptly make his announcement over Twitter. Macron's visit could prove critical to swaying Trump toward a compromise, rather than the all-or-nothing approach he has signaled on the Iran deal. The French leader -- who has been dubbed a "Trump whisperer" by some -- has forged one of the closest relationships Trump maintains with any world leader, some of whom he has openly feuded with or belittled.

That "Trump whisperer" status was on full display ahead of his visit to the US, when Macron appeared on Fox News -- Trump's favorite network -- to make an early case on the Iran deal, as if speaking directly to the President.

"What do you have as a better option? I don't see it," Macron said of the deal, which he acknowledged is not "perfect." "What is the what-if scenario or your plan B? I don't have any plan B for nuclear against Iran. So, that's the question we will discuss."

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The appearance on Fox continued Macron's pattern of assiduously cultivating Trump using flattery and a careful study of his likes and dislikes. In July, he correctly guessed that a military parade down the Champs-Élysées might appeal to his US visitor; Trump liked it so much he ordered the Pentagon to plan a similar one back home.

But beneath the outward bonhomie is an underlying competitiveness, according to US and French officials familiar with the two men's relationship. Both are alpha males highly attuned to their own reputations, and each entered office with grand promises of shattering their country's political status quo. Officials in both countries have downplayed the notion of a "bromance," insisting the two men are not close personal friends but rather closely aligned allies.

Ever since May, when the two men met for the first time inside the US ambassador's residence in Brussels, fascination has swirled around their relationship. That first meeting was marked by strained grins and a lengthy, white-knuckled handshake that immediately went viral online.

Even before that session, which occurred on the sidelines of a NATO summit, Macron has carefully approached his interactions with an unpredictable American leader. He studied videos of Trump's handshakes, which sometimes include a firm tug inward. And he and his aides continue to closely monitor Trump's Twitter feed for a daily reading of the US President's mood and his shifting policy sentiments.

Contrast with Merkel

Perhaps most shrewdly, Macron recognized that Europe's other dominant leader, German Chancellor Angela Merkel, would be permanently tarnished in Trump's mind after fostering deeply personal ties to President Barack Obama. Long averse to his predecessor's policies and platforms, Trump has viewed Merkel as irrevocably tied to Obama, according to people who have spoken to him.

Macron has cast himself as a blank slate, without a pre-existing relationship that might color his interactions with Trump (though Macron has met privately with Obama, and even secured Obama's endorsement during his campaign last spring).

Merkel will visit the White House on Friday with none of the elaborate trimmings associated with a state visit. Once the favored European leader for US presidents, including Obama and President George W. Bush, Merkel got off to a frosty start with Trump and struggled to recover. The two leaders went more than five months without speaking earlier this year.

That's left an opening for Macron, who has deployed flattery and a close study of Trump's mindset to secure a position as the chief transatlantic emissary, reasserting Paris as the principal European contact point after long being overshadowed by Berlin and London.

That was on heightened display earlier this month as the two men worked closely to plan retaliatory strikes for a suspected chemical gas attack in Syria. Early in the week, US administration officials rushed to develop plans for a response amid concerns Macron would act first. Trump told his advisers that he didn't want to appear to play second fiddle to his younger French counterpart.

Syria policy

As the week proceeded, however, the two men spoke almost daily to develop a response, alongside British Prime Minister Theresa May. After the strikes, Macron even claimed during a television interview that he had "convinced" his US counterpart to remain committed to Syria, despite his declaration that US troops would soon exit the country.

But it appears Macron will need to press his case again in person. Even in the wake of the strikes against the Syrian regime's chemical weapons facilities, the White House refused to walk back Trump's decision to prepare for withdrawal.

"Our policy hasn't changed," White House press secretary Sarah Sanders said last week in response to Macron's claim. "We still have troops on the ground. But the President wants to bring those people home, and that hasn't shifted."

Top US military officials and US allies who are invested in the region have worried that a withdrawal of US troops -- who are explicitly involved in the fight against ISIS -- could create a vacuum for Russian and Iranian influence to expand in the region.

Even as Trump has warned of a "sustained" response to the use of chemical weapons in Syria, the US has yet to impose fresh sanctions targeting Russian companies that have facilitated Syria's chemical weapons program. A senior administration official said Friday the sanctions were still under consideration, but said it was uncertain whether new sanctions could be announced to coincide with Macron's visit.

As he headed toward Washington on Monday, Macron spoke by phone with Russian President Vladimir Putin to discuss Syria and other matters.

Trade is also expected to be on the agenda, with the steel and aluminum tariffs Trump signed into law expected to hit exempted European allies on May 1 unless the parties reach a deal averting the tariffs.

"I hope ... he will not implement these new tariffs and he will decide for an exemption for the European Union. You don't make trade war with your ally," Macron said in his Fox News interview. "I'm an easy guy. I'm very simple. I'm straightforward. It's too complicated -- if you make war against everybody. You make trade war against China, trade war against Europe, war in Syria, war against Iran -- come on, it doesn't work. You need ally. We are the ally."