The Metropolitan Museum of Art’s new show “Sargent and Paris” (April 27–August 3) explores John Singer Sargent’s early career, before and after that infamous portrait of Madame X in 1884.

“Sargent showed this portrait soon after his Madame X statement. And it’s proof that he was not going away,” Herdrich says. “The last gallery in the exhibit is for his work post–Madame ...