Ringside for the longest handshake in politics
Their first handshake was a genuinely white-knuckle affair, with Emmanuel Macron gripping hold tightly of Donald Trump in order to let him know it was "a moment of truth".
Since then, they've worked on their greetings, appearing much more at ease, and a little less macho.
When they shook hands after Mr Macron and his wife, Brigitte, met Mr Trump and Melania at Les Invalides in Paris last week, it appeared to last considerably longer than their first - long enough, indeed, for Mr Trump to tell the French First Lady she was in "great shape".
Yet nobody was ready for the most recent Trump-Macron 'poignee de mains', a strange, shifting coming together that appeared to have a life of its own.
Many who witnessed the handshake, as the pair of presidents walked tall down the Champs-Elysees, said that it looked awkward. But it appeared anything but awkward for Mr Trump, who was so at ease with his French host and the Bastille Day crowds, that the handshake lasted up to 30 seconds.
Twelve seconds into the handshake - by now with the two men on the move - Mr Trump puts one hand on Mr Macron's chest.
A few moments later, he places his left arm on the shoulder of Ms Macron, while still holding on her husband with his right.
Then he briefly takes the French First lady with both hands, while Mr Macron keeps holding on to Mr Trump's right hand as well. Finally, with the timer on 28 seconds, Mr Trump grips Mr Macron's hand once more, taps his fingers and finally lets him go.
A full half-minute of presidential flesh-pressing has taken place.
It is difficult to know what Melania Trump made of this manual menage a trois.
She was watching and smiling a full 30 seconds before her husband and the Macrons appeared to realise she was there. Then they held hands with her, too.