Kevin Harrison (Robert Wagner), a corrupt arms dealer, attempts to destroy an American-owned Concorde on its maiden flight after one of the passengers, reporter Maggie Whelan (Susan Blakely), learns of his weapons sales to communist countries during the Cold War.
The Concorde takes off from Charles de Gaulle Airport in Paris. Captain Paul Metrand (Alain Delon) makes conversation with Isabelle (Sylvia Kristel), the purser. They land at Dulles Airport outside Washington, D.C.
Maggie reports on the "Goodwill" flight on the Concorde the following day, which leads to a story of Harrison and his Buzzard surface-to-air missile project. A man named Carl Parker (Macon McCalman) shows up with a claim about documentation of illegal arms deals, but is shot before a passerby triggers a fire alarm, scaring the assailant away.
Maggie is told by Harrison someone is framing him. He sends Maggie off in a limo, then plots to have the Concorde's departure delayed and the drone test reprogrammed.
Capt. Joe Patroni (George Kennedy) joins Metrand aboard the Concorde, creating some doubt as to which pilot is in command. They are joined by Peter O'Neill (David Warner), the 2nd officer and flight engineer, who is living with a controlling girlfriend.
Harrison surprises Maggie at the airline check-in desk to see her off. He asks if the documents showed up, but they have not. As he is walking away, Parker's wife delivers the documents to Maggie as she steps into the mobile lounge. She looks them over and realizes that Harrison lied to her.
The Concorde takes off for Paris. Unbeknownst to the flight crew, an off-course surface-to-air missile is headed straight for them. At his company headquarters, Harrison tells his controllers to alert the government. The USAF scrambles F-15 fighter jets to intercept the missile just as it locks onto the Concorde. After several evasive maneuvers by the passenger plane, an F-15 shoots down the missile before it collides with the Concorde.
As the Concorde is approaching the European coastline, an F-4 Phantom II sent by Harrison engages the Concorde as French Air Force Mirages scramble to help. The Concorde manages to evade the F-4's missiles, but the explosion of one of them damages the plane's hydraulic system. The Mirages shoot down the F-4 and the Concorde continues to Paris, although to Le Bourget airport instead of Charles de Gaulle. The plane reaches the French coastline, landing with a damaged hydraulic system and just barely stopping at the last safety net. Metrand and Isabelle invite Patroni to dinner.
Harrison promises Maggie to go public with the documents but attempts to bribe her into "polishing" his statement. After being paid by Harrison, a mechanic, Froelich (Jon Cedar), places a device in the Concorde's cargo door control unit, timed to open during flight.
As the passengers board, a well-dressed woman (played by Charo) attempts to smuggle a dog aboard. She is caught by an alert Isabelle and leaves. Froelich is in line at the security checkpoint when some of his money falls out of his pant leg. The X-ray technician attempts to return it, but Froelich pretends not to hear and runs off panicked. On the runway, where the Concorde is taking off, the aircraft's exhaust kills Froelich and scatters the money he received from Harrison.
The aircraft is en route to Moscow when the automatic device opens the cargo door. Metrand sees the carpet tear down the middle of the aisle, signifying the fuselage is under tremendous stress and the aircraft is about to break apart. The cargo door is ripped off, extensively damaging the aircraft and ripping a segment of the floor as it spirals toward the ground. The airline founder's seat lodges in the hole, acting as a plug. The pilots attempt to fly to Innsbruck, Austria for an emergency landing, but realize they are losing fuel and do not have enough to make it there. Metrand realizes they are flying towards a ski area he knows in the Alps; they could make a gear-up landing on a mountain-side.
The aircraft approaches the landing site while the ski patrol marks a runway. It lands successfully. While passengers are being rescued, Maggie gives a report of the accident to a news reporter and mentions a major story she is about to release. Harrison is seeing the newscast in his private plane and commits suicide. At the crash site, the last of the crew leaves the Concorde shortly before the fuselage caves in and explodes from the leaking fuel.
Who commits suicide?
Harrison