"Something could happen with respect to the Paris accords, let's see what happens", Trump told a news conference.
Eventually, the three were joined by the first lady Melania Trump for a four-way handshake.
Protesters have been carrying banners with crossed-out names and portraits of the United States leader on them.
With his free hand, Macron rather awkwardly points to something for Trump to look at, all the while continuing with the handshake. Even then, Mr Trump held on to Mr Macron as he shook hands with his wife, Brigitte.
Trump also performed a prolonged handshake with Macron upon meeting him in Brussels in May.
In the video, U.S. president did not hide his actions, even appearing to take a step back to appraise the French president's 64-year-old wife. "America and France will never be defeated or divided", he said.
Weeks after Macron hosted Russian President Vladimir Putin at the Palace of Versailles, Trump will bask in the trappings of the Bastille Day military parade on Friday and commemorations of the entry 100 years ago of USA troops into World War One.
Despite major differences between the two leaders on such issues as climate change and trade, Mr Macron nonetheless carved out time to lead Mr Trump on a tour of the Les Invalides monument.
Trump reportedly requested military hardware to be included in his inaugural parade, though ultimately the usual mix of marching bands processed down Pennsylvania Avenue instead of tanks and troops.
Trump's trip has included a gilded tour of one of France's most storied monuments and dinner at the Eiffel Tower.
There was some waving of Emmanuel's fist and a weird pat of his chest before the president leaned over and kissed Brigitte Macron goodbye, taking her hand in his free hand.
There, the USA president complimented 64-year-old Brigitte Macron, saying: "You know, you're in such great shape. handsome".
It's unclear whether Trump and Macron are using a show of physical strength against each other during their extensively photographed greetings and exchanges, or if the two presidents' handshakes are simply the awkward gift that keeps on giving for viewers across the globe.
Today's celebrations in Paris were tinged with mourning, coming a year on from a jihadist massacre that claimed 86 lives in the southern city of Nice, where Macron led remembrances after the Paris ceremonies.