The parade, which marked 100 years since the U.S. joined World War I, was used by French President Emmanuel Macron to emphasise the ties between the two countries and their shared interest in combating terrorism, including in the Middle East. Then, appearing to turn to Macron, he remarks, "she's in such good physical shape".
The whole thing took place while the Trumps were touring the Hôtel National des Invalides, which houses the tomb of Napoleon Bonaparte.
"We will talk about that over the coming period of time and if it happens, that will be wonderful, and if it doesn't, that'll be okay too", he added.
While still clasping Macron's hand, meanwhile, he also grabs the hand of Macron's wife, Brigitte and kisses her on the cheek before eventually letting Macron go.
As they were saying goodbye, Mr Trump turned to Brigitte Macron and gestured towards her body.
"So, I really have a feeling you are going to have a very, very peaceful and lovely Paris".
The Paris celebrations of Bastille Day are expected to end with a spectacular fireworks display fired from near the Eiffel Tower.
Their parting handshake Friday, after a brief Paris visit by Trump as questions exploded about his family's meetings with Russian Federation, was possibly the strangest yet.