Current and former officials say the surveillance on the Kouachis had turned up nothing to indicate that they were an imminent threat. They point to the lack of resources to conduct physical surveillance on large numbers of targets, estimating that 25 agents, working in shifts, are required to watch over a single person day and night.

“You can’t follow everyone,” said Bernard Squarcini, who was Mr. Calvar’s predecessor as head of the domestic intelligence agency and was in charge when the Kouachis were placed under surveillance after a tipoff from the United States in 2011. “These were two inactive targets that had been quiet for a long time. They were giving nothing away.”

Others were less forgiving. “Even if you give France a bit of a break,” said one former senior United States counterterrorism official, who spoke on the condition of anonymity to avoid antagonizing an ally, “given what we know, and what the French knew then, these guys should have been high on any list. Especially since they seemed to have all the warning signs: travel to the region, a prison record, a social media profile. What more did they need?”

At the very least, the Charlie Hebdo attack has provoked a fundamental debate about the quality of intelligence gathering in France. Long considered among the best in the world, French intelligence has been troubled by three high-profile failures in four years: Before the Kouachis and the Nemmouche case, there was Mohammed Merah, a French-Algerian whose surveillance had been dropped shortly before he shot seven people in Toulouse in March 2012.

Image From left: Salim Oman Benghalem, who traveled to Yemen; Peter Cherif, who also traveled there. Credit... From left: LeMonde; Benoit Peyrucq/Agence France-Presse

At a time when budget cuts and debates over the balance between national security and personal liberty are making the trade-offs for security forces even more complex, the case of the Kouachis stands out. They were well known to the authorities in the United States as well as France before the radical group known as the Islamic State came on the scene — and they struck just when the authorities had turned their attention to the threat posed by the new generation of jihadists inspired by the group, also known as ISIS or ISIL.

Interviews with current and former French and American officials and other experts provided new details about key moments and the lapses, misunderstandings and turf issues that characterized the case.