While on a prolonged European getaway following a medical conference in Paris, American doctor Ben McKenna (James Stewart) is accompanied by his wife Jo (Doris Day) and their young son Hank (Christopher Olsen). During their bus journey in French Morocco, a moment unfolds when Hank inadvertently removes the veil from a Muslim woman, which nearly sparks an international incident. Fortunately, Louis Bernard (Daniel Gélin), a French bystander, steps in to diffuse the situation, much to Ben's relief. He eagerly opens up about his family and their upcoming sightseeing plans in Marrakech, although Jo grows increasingly wary of Louis's inquisitive nature.
Later that evening, the McKennas invite Louis to their hotel for dinner; however, he abruptly cancels their plans when faced with the threat of Rien (Reggie Nalder), a hired killer, appearing at their doorstep. In a twist of fate, the McKennas find themselves dining with a British couple, the Draytons (Bernard Miles and Brenda de Banzie), who profess admiration for Jo's vocal talents from her pre-marital days.
The next day in the bustling marketplace, the atmosphere drastically shifts as a man, fleeing from the police, collapses fatally wounded in Ben's arms. It is Louis, disguised as an Arab, who manages to convey, with his dying words, that there is a conspiracy to assassinate an unnamed statesman in London. He urges Ben to reach London quickly to inform the authorities about "Ambrose Chapel."
While being questioned at the police station, Mrs. Drayton offers to look after Hank. It's revealed that Louis was actually a French spy. Just then, Ben receives a chilling phone call from a mysterious figure who cruelly informs him that Hank has been kidnapped, threatening harm unless the McKennas keep quiet about Louis's last message. When they return to their hotel, Ben learns that Mrs. Drayton has not yet returned with Hank, and Mr. Drayton vacated the premises only moments ago.
After administering a sedative to the agitated Jo, Ben must break the horrifying news that their son has been taken. Realizing that the Draytons departed on a private plane, the desperate parents resolve to travel to London in search of Hank. Upon arriving at the airport, they are met by a throng of fans and the police, including Inspector Buchanan (Ralph Truman), who reveals he knows exactly why their son has been abducted. Ben, determined to protect Louis's secrets, refuses to divulge his final words, citing confusion regarding the French language.
In London, after a brief phone conversation with Hank courtesy of Mrs. Drayton, the McKennas check into a hotel. As they try to connect with Ambrose Chapel, their plans are disrupted by the appearance of Jo's old friends: Val and Helen Parnell (Alan Mowbray), Jan Peterson (Hillary Brooke), and Cindy Fontaine. As Jo stays behind with her friends, Ben stealthily sneaks out to track down Ambrose.
At Ambrose's taxidermy shop, Ben quickly discovers that neither Ambrose Sr. nor Ambrose Jr. is involved in his son’s disappearance, necessitating a hasty getaway as law enforcement arrives. Meanwhile, Jo uncovers that Ambrose Chapel refers to a location, leading her to meet Ben there.
Inside the church, they find Hank being held captive by the Draytons, leaders of an anarchist group, with an accomplice named Edna overseeing him. Furthermore, Rien awaits instructions on the precise moment to carry out the assassination at an upcoming concert at Albert Hall.
As the McKennas slip into the chapel just as the service led by Mr. Drayton is commencing, Ben remains inside while Jo leaves to summon the police. However, when Drayton cuts the service short, Ben rushes to save Hank, only to be knocked out by the villain's brute force. By the time authorities arrive, the Draytons have made a clean escape with Hank. With the police unable to act without a search warrant, Jo desperately seeks help, only to discover Buchanan is tied up at a diplomatic function during a concert.
Simultaneously, Ben escapes his confines and heads to the concert as well. Spotting Rien poised to assassinate the foreign prime minister, Jo yells, inadvertently causing him to miss, wounding the dignitary instead. Ben seizes the opportunity to confront Rien, leading to the assassin’s tragic fall to his demise.
Later, while the Draytons hide out in the embassy, their employer, the ambassador (Mogens Wieth), informs them that their assassination attempt has failed. Under pressure from Mrs. Drayton, the ambassador orders that they kill Hank. With the police unable to intervene due to a stipulation concerning diplomatic immunity, the McKennas bravely decide to enter the embassy as guests of the grateful prime minister.
Jo performs for the guests, and her voice reaches Hank, allowing him to whistle along, guiding Ben to his son’s location. Just when it seems like disaster strikes, Ben manages to push Drayton away, leading to his own downfall.
In a heartwarming conclusion, the reunited McKennas return to their hotel, where Jo's friends have been anxiously awaiting them throughout their ordeal.
