At the Académie André in France, an older woman named Madame Hélène watches students with a discerning eye to protect the reputation of her beloved institution from slander. An American veteran who is studying there in the 1950s gets into her good graces by voicing his genuine thoughts and admiration. Nebraska is an honest, quiet thirty-year-old man who has a tendency to keep to himself. Madame Hélène notices that the begins to change once he attracts the attention of a young woman named Anna Barkova, who has a playful spirit. Nebraska has been drawing portraits of her face in his notebook because her haunting eyes have drawn his attention. Anna learns that he is drawing her. After that, she begins to hang around Nebraska, even though he would rather her not do so. He gets anxiety about her flirtations with him, but she does not seem to pick up on them. She makes a habit out of following him when he makes a habit of viewing a commemoration of a student who died in the war. Nebraska begins to enjoy Anna's company, engaging in playful banter and allowing her to have sketches he draws. Although he likes Anna, he does not like her friend Bernard, who seems harshly anti-American. He is an incredible artist, however, who makes horrifying drawings on newspapers.

One day Nebraska walks in on Anna sharing his sketches with Bernard while Bernard mocks them in front of other students. This upsets the man. After that, Nebraska stays away from the Académie for more than a week. When he returns, Madame Hélène pulls him aside and asks him to take Anna to coffee because Bernard committed suicide and she needs a friend. Nebraska agrees. While they are walking there, Anna insists on walking on the side of the street nearest cars, even though Nebraska thinks it is not ladylike. Her playful nature seems unharmed.

Later, while they are both in the studio, a model speaks German unexpectedly. This elicits a strong reaction from Anna and Nebraska asks her if she wants to go get coffee. Once they get there, her playful demeanor finally drops and she details how most of her family and friends died during the Holocaust at the hands of the Nazis. She tells about how her father used to tell her and her sister that someday a car would come to take them to America and that was why he always walked near the street. Bernard was one of her only friends who survived. His family died in concentration camps.

Nebraska proposes marriage and says they can move to America together. Anna considers it, but is soon dissatisfied when he expresses his thoughts about art and she remembers her friend Bernard. They walk home and she seems more like an adult. She tells Nebraska that she has no desire to live in America. Madame Hélène sees them when they arrive back at the Académie.