An American woman named Phoebe finds herself in the enchanting streets of Rome, Italy, after her Italian boyfriend, Marcello, eagerly invited her over to join him. However, upon her arrival, her dreams are shattered when he refuses to take her calls, leaving her heartbroken and alone in the city's vibrant atmosphere. In her wanderings, she encounters a mischievous dachshund decked out in an opulent plaid coat, who swiftly snatches her lunch away. Despite her attempts to shoo the dog away, Phoebe soon discovers a newspaper advertisement offering a staggering $5,000 reward for the return of the lost dachshund, belonging to the affluent Madame Van Dougen, who resides in glamorous Monte Carlo, Monaco.
In another part of town, another American, Julian Peters, finds himself abruptly terminated by his Italian acting agent. As fate would have it, the same lost dachshund approaches him for food, revealing an expensive collar with "Monte Carlo" emblazoned on the name tag. When Phoebe stumbles upon Julian with the dog, she tries to claim it as her own, yet Julian doubts her sincerity, suspecting her of scheming for the reward money. After some negotiation, she reluctantly agrees to split the reward, and together they board a train headed for Monte Carlo.
On the train, American couple Neil and Marilyn Schwary are embroiled in a debate about Neil's supposed "winning" system for roulette. Their conversation is interrupted by the affable but regretful recovering gambling addict, Augie Morosco, who is traveling to reconnect with his wealthy wife, Elena, in Monte Carlo. Shortly afterward, Phoebe spots Augie holding the coveted dachshund and accuses him of stealing it. Augie, however, insists that he purchased the dog from a man in the dining car, causing Phoebe to fume with frustration. In a twist of events, Augie allegedly paid Julian $6,000 for the animal. Furious at the betrayal, Phoebe demands they return the payment and ensure the dog is delivered to its rightful owner.
As events unfold aboard the train, Augie finds himself in a precarious position when a train porter insists on viewing the dog’s travel papers. Faced with scrutiny, Augie returns the dog to Julian and advises him to meet him in Monte Carlo should Julian change his mind about the sale, handing him a matchbook bearing his name. Meanwhile, tensions rise as Julian interferes with other passengers' affairs and ends up having to phone Madame Van Dougen to notify her of their delay after encountering unexpected challenges.
Meanwhile, as Marilyn dons a stunning gown from Neil’s clothing business, she catches the attention of the dashing Alfonso de la Pena. Neil, blinded by his fixation on gambling, brands her a "jinx" and attempts to deter his wife's social interactions. In a twist of luck, Marilyn wins a significant sum while playing craps with Greek gambler Hercules Popodopoulos, but Neil spirals into despair as he loses his entire bankroll. He turns to Augie for help, leading them to make a fateful bet together just as Elena storms in, upset over Augie's slip back into gambling.
After reaching Monte Carlo, Phoebe's fury towards Julian simmers as they seek Madame Van Dougen’s villa only to discover it vacant. Upon exploring the property, they stumble upon her lifeless body in a garage, their panic intensifying as they realize the gravity of their situation. Julian, overwhelmed with dread, refrains from going to the police, fearing they’ll be wrongly accused due to their foreign status. A tense kiss shared between them masks their anxiety as they blend into the crowd, but soon they decide to contact law enforcement anonymously.
As the investigation unfolds, Neil and Marilyn aim to distance themselves from their own troubles but inadvertently find themselves tangled in the events surrounding Madame Van Dougen's murder. The suitcase Neil steals from a parked car complicates matters further when it reveals a shocking secret. As all parties converge at the police station, the unfolding drama pits them against Inspector Bonnard, who methodically unravels the various tangled truths and claims of innocence.
The police inquiry intensifies when Bonnard reveals discrepancies in the accounts of Madame Van Dougen's housekeeper and butler, leading to a confession that exposes the darker motives underlying her murder. In an unexpected twist, all the American characters’ paths intertwine as they celebrate their release over dinner with Bonnard, who reflects on the bizarre events that brought them together. Julian, in a moment of realization, toasts to the dachshund, Napoleon, for his role in reuniting him with love and perhaps a fortune, as Madame Van Dougen’s legacy lives on through her unique and unsuspecting heir.
Finally, the film closes on a sly note with Alfonso basking in luxury on a yacht while sipping champagne alongside Napoleon, suggesting that not all partiers face the consequences of their actions.
