Ambling onto the Art Deco set of “The Tonight Show” for his monologue rehearsal one Monday afternoon, Jimmy Fallon gave the crowd here at Studio 6B a warm, practiced welcome before trying out a new batch of jokes about the French election, the pop star Harry Styles and President Trump’s definitions of medical terms. “He thinks a cardiologist is someone who works at Hallmark,” he quipped.

Wearing casual clothes and a boyish smirk, Mr. Fallon made a pitch for his program’s vision. “Anything I can make fun of, I will make fun of,” he told his audience. The late-night entertainment being fine-tuned in front of them, he added, had been devised so that “you go to bed with a smile on your face and you have sweet dreams.”

Then he stepped to the spot where he delivers his monologue each evening and noted that the stage mark was in the shape of a four-leaf clover. “I’m Irish,” he explained, “and I need all the luck I can get.”

It was a throwaway, self-deprecating line, but also an accurate self-assessment from Mr. Fallon, 42, who is in his fourth year of hosting “The Tonight Show,” NBC’s flagship late-night program.