Peter P. Peters (Fred Astaire), an American ballet dancer billed as "Petrov", dances for a ballet company in Paris owned by the bumbling Jeffrey Baird (Edward Everett Horton). Peters secretly wants to blend classical ballet with modern jazz dancing, and when he sees a photo of famous tap dancer Linda Keene (Ginger Rogers), he falls in love with her. He contrives to meet her, but she is less than impressed. They meet again on an ocean liner traveling back to New York, and Linda warms to Petrov. Unknown to them, a plot is launched as a publicity stunt "proving" that they are actually married. Outraged, Linda becomes engaged to the bumbling Jim Montgomery (William Brisbane), much to the chagrin of both Peters and Arthur Miller (Jerome Cowan), her manager, who secretly launches more fake publicity.