Patricia Harper, the heiress daughter of billionaire oil tycoon James Harper, dines with Mrs. Isabel Channing and Elliott Winthrop, and her wish for a simple, ordinary life clashes with Mrs. Channing’s insistence on propriety. When Elliott announces his promotion to U.S. ambassador to France, he is summoned to the consulate to handle a problem at the gate, setting the stage for a curious encounter.
At that gate, Buck Boswell and his American dance troupe arrive, seeking an emergency return to the United States. Elliott explains that the budget has no room for such a flight, but Buck isn’t easily deterred. He promises the troupe they’ll find a way home and, to secure their current situation, leads them to an upscale hotel. The staff are impressed by the troupe’s bravado and the illusion that Americans always pay—so the troupe moves in, even though they don’t actually have funds to cover the stay. The hotel owner, dazzled by the idea of wealthy guests, allows it, much to the dismay of his wife.
The next day, the hotel's wife, irked by the unpaid bill, locks the troupe out of their rooms. To regain their belongings, the girls pressure the guys to find work, and Buck is handed a mere 5 francs by one of the girls—the last bit of money left to the group. Their predicament pushes Buck to cross paths with Patricia Harper, who recognizes him by his cowboy garb and asks him to cover a small breakfast bill she claims to have left in her hotel room. She claims to have money, but she keeps it hidden, and her act of "two strangers, one chance" draws Buck into a partnership with the troupe.
Back at the hotel, Patricia pretends to be suicidal to lure the staff onto the roof, hoping to obtain the keys to their rooms from the chaos below. The ruse works briefly, but the hotel staff, now alerted, call the police. Patricia’s father arrives after he’s alerted to his daughter’s disappearance, and the troupe makes a dramatic escape by climbing from one building to another.
The ensemble ends up in an old studio full of mannequins, which they believe to be abandoned. They spend the night there, and upon waking, they overhear chatter that reveals a coming show at a theater. A mix-up with a Russian troupe occurs, and Buck, thinking he’s a producer, ends up guiding his own troupe into the Russians’ place on stage.
Meanwhile, Patricia’s father spies royal jewels in a display at his hotel and attempts to purchase them, only to be refused. He then steals them, triggering a manhunt for jewel thieves that threads through the rest of the plot. A replica necklace, crafted as a gift for Patricia by her father, enters the scene, and Buck, suspicious of her father, hides the replica and later discovers it.
A tense exchange at the hotel follows, and a chance encounter with a man who turns out to be an oil magnate leads Buck to misinterpret a deal and tear up a contract. Realizing that his best chance to return home is to return the jewels, he crafts a plan to navigate the French authorities by presenting the jewels as a rightful offering. The plan goes awry when the jewels are discovered to be replicas, and Buck finds himself imprisoned for a time while the troupe is hunted.
The final act sees Buck breaking free, racing to confront Patricia and her father during a dinner with Elliott and Ms. Channing. A scuffle ensues; the jewels end up stranded on a roof, but Buck retrieves them, and the troupe is arrested. At the police station, their true identities are revealed and they are released. In the end, Buck and Patricia choose each other, sealing their union with marriage, and the entire escapade resolves into a hopeful finale of truth and togetherness.
