Observers and critics used a snippet of digital footage as a way to show that she might be out of her depth: A short video posted to Instagram by the office of Emmanuel Macron, the president of France, showed Ms. Trump in conversation with Theresa May, the departing prime minister of Britain, and Christine Lagarde, the International Monetary Fund managing director, as Mr. Macron and Justin Trudeau, the Canadian prime minister, listened.

In the clip, Ms. Trump seemed to be looking to find a place to jump into this diplomatic game of double Dutch. First Mrs. May spoke: “As soon as you charge them with that economic aspect of it, a lot of people start listening who otherwise wouldn’t listen.”

And then Ms. Trump jumped in: “And the same with the defense side of it, in terms of the whole business that’s been, sort of, male-dominated.”

Ms. Lagarde, who was standing next to the president’s daughter, swiveled her head and blinked several times as she listened.