Moments later, as they sat side by side, Mr. Macron placed his hand on Mr. Trump’s knee.
Theirs was not an enduring bond. As Gérard Araud, France’s former ambassador to the United States, recently said on Twitter, Mr. Macron focused on placating the president “because Trump is the most powerful guy on earth.”
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“Most presidents tend to exaggerate the significance of personal relationships,” said Richard N. Haass, the president of the Council on Foreign Relations. “Personal connections can decrease the odds differences become crises — but all the personal chemistry in the world cannot turn differences into agreements.”
By contrast, Mr. Macron, 44, and Mr. Biden seem to enjoy each other. They saw each other only a few weeks ago, when both traveled to Bali, Indonesia, to attend the Group of 20 summit.
During one event, where they planted baby mangroves and toured a mangrove farm, the two stayed close to each other, talking intently as other leaders examined the plants. At one point, they were asked if they had any reaction to Mr. Trump announcing a run for the presidency in 2024. The two looked at each other and shared the faintest of smiles.
“No, not really,” Mr. Biden said, before they continued on their tour.
In September, when they met in New York on the sidelines of the General Assembly of the United Nations, their discussion, originally scheduled for 10 to 15 minutes, stretched to almost an hour.
The pair are not particularly opposed in their worldviews, but Mr. Macron and Mr. Biden have engaged in an explosive quarrel. There was the scuttling of a nuclear-powered submarine deal, which led France to pull its ambassador from Washington. (“Trust is like love; declarations are good, but proof is better,” Mr. Macron said last year when Mr. Biden admitted to committing an act of clumsy diplomacy.)
They also do not agree on Mr. Macron’s so-called strategic autonomy plan to make Europe less dependent on the American military, nor do they see eye to eye on Mr. Biden’s plans to offer preferential treatment to U.S. automakers that make electric vehicles.