They were among 360 people seized by Iraqi troops after their plane made an unplanned landing in Kuwait as Saddam Hussein's forces launched their invasion of the Gulf state in the early hours of 2 August 1990.
The ruling, by France's highest court, ended a long-running dispute in which the passengers accused the airline of making an unscheduled stop to drop off British commandos and pick up British intelligence agents operating in Kuwait - a charge both the British government and BA denied.
A judge at the Cour de Cassation, in Paris, ruled yesterday that BA's customers had been "exposed without reason" to the risk of war and that the airline had failed to ensure their security.
BA, which was fined pounds 4m earlier this week in a separate case, after breaking EU competition rules, was appealing against a ruling that was first delivered by the French courts four years ago.
A spokesman for the airline said it was disappointed at the ruling, adding that it contradicted similar cases in British courts and meant the company was being held responsible for events beyond its control.
"The decision differs from the interpretation of courts in other countries," he said.
"We have said throughout that while we have every sympathy for those taken hostage, what happened to them was the result of an act of war by Iraq which took the whole world by surprise. We could not have foreseen it and should not be held responsible for its consequences."
Flight BA149 was en route from London to Kuala Lumpur, the capital of Malaysia, when it landed in Kuwait at 1.18am.
But Iraq had declared war on the Gulf state just a few hours earlier, and when the plane landed, the Iraqis, who were controlling the airport, took the passengers and crew hostage.
Some of the hostages were held for nearly three months, and most were used as human shields to protect strategic sites from potential bombing by US-led forces. The aircraft, a Boeing 747, was destroyed during the war.
The case was first brought before the courts in 1995, when a French judge held that BA was entirely responsible and ordered a payment of pounds 40,000 to each hostage held for up to a month, pounds 60,000 to those detained for up to three months and pounds 6,000 each to 48 family members.
BA appealed against the decision, but it was upheld the following year, when a judge said that the British airline had "exposed its passengers in a reckless manner to a risk of war".
The French passengers' campaign was led by Paul Merlet, an anaesthetist from Nantes, who was the last person to be freed by Iraq.
Mr Merlet, his wife, Monique, and their teenage son spent three months being shuttled from one strategic site to another before they were released.
In a similar case in 1991, after the US district court in Galveston, Texas, heard evidence in camera, British Airways paid compensation to American passengers.Reuse content