ISLAMABAD/NEW DELHI šC Just after midnight on May 7, the screen in the Pakistan Air Force¡¯s operations room lit up in red with the positions of dozens of active enemy planes across the border in India.

Air Chief Marhall Zaheer Sidhu had been sleeping on a mattress just off that room for days in anticipation of an Indian assault.

New Delhi had blamed Islamabad for backing militants who carried out an attack the previous month in Indian Kashmir, which killed 26 civilians. Despite Islamabad denying any involvement, India had vowed a response, which came in the early hours of May 7 with airstrikes on Pakistan.

Sidhu ordered Pakistan¡¯s prized Chinese-made J-10C jets to scramble. A senior Pakistani Air Force (PAF) official, who was present in the operations room, said Sidhu instructed his staff to target Rafales, a French-made fighter that is the jewel of India¡¯s fleet and had never been downed in battle.

¡°He wanted Rafales,¡± said the official.

The hourlong fight, which took place in darkness, involved some 110 aircraft, experts estimate, making it the world¡¯s largest air battle in decades. The J-10s shot down at least one Rafale, U.S. officials said in May. Its downing surprised many in the military community and raised questions about the effectiveness of Western military hardware against untested Chinese alternatives. Shares of Dassault, which makes the Rafale, dipped after reports the fighter had been shot down. Indonesia, which has outstanding Rafale orders, has said it is now considering purchasing J-10s ¡ª a major boost to China¡¯s efforts to sell the aircraft overseas.

But interviews with two Indian officials and three of their Pakistani counterparts found that the performance of the Rafale wasn¡¯t the key problem: Central to its downing was an Indian intelligence failure concerning the range of the China-made PL-15 missile fired by the J-10 fighter. China and Pakistan are the only countries to operate both J-10s, known as Vigorous Dragons, and PL-15s.

The faulty intelligence gave the Rafale pilots a false sense of confidence they were out of Pakistani firing distance, which they believed was only around 150 kilometers, the Indian officials said, referring to the widely cited range of PL-15¡¯s export variant.

¡°We ambushed them,¡± the PAF official said, adding that Islamabad conducted an electronic warfare assault on New Delhi¡¯s systems in an attempt to confuse Indian pilots. Indian officials dispute the effectiveness of those efforts.

¡°The Indians were not expecting to be shot at,¡± said Justin Bronk, an air warfare expert at London¡¯s Royal United Services Institute (RUSI) think tank. ¡°And the PL-15 is clearly very capable at long range.¡±

The PL-15 that hit the Rafale was fired from around 200 km away, according to Pakistani officials, and even...