'Certified Copy' opens with a shot of a book propped up on a table with two microphones and two glasses of water, ready for a guest lecturer to come discuss his latest work. The book, which the movie is named for, shows two Grecian-style statues staring at each other sightlessly. It is about how art reproductions create their own worth, according to the author's theory, by leading us to their original. These fakes are themselves certified, in their own way, as originals.
Later, this author, James Miller (William Shimell), meets a woman from the audience, Elle (merely "she" in French, as played by Juliette Binoche), in her antiques shop for a coffee date. What was at first an awkward sort of meeting between strangers, with Elle ducking her head and offering him a tour of her shop, slowly becomes antagonistic as they discuss his theories. It's confusing and discomfiting, and stranger still, these discussions suddenly dive dizzyingly into personal territory. James and Elle slip into a familiar patter easily recognizable by anyone who's ever been in a long-term relationship as they travel to a small village in Tuscany before James has to catch his train.