Among the signs pointing to Al Qaeda is the fact that a recent issue of Inspire — the propaganda magazine published by the Yemen affiliate of the group, Al Qaeda in the Arabian Peninsula — named Charlie Hebdo’s editor, Stéphane Charbonnier, to its suggested hit list of Westerners who have insulted the Muslim faith. His name appears in a two-page spread under the heading, “A Bullet a Day Keeps the Infidel Away — Defend the Prophet Mohammed.”

There were signs that the assailants had received military-style training. Two of the gunmen are seen in video footage moving across a narrow Parisian street shadowing each other, and also gripping their weapons correctly, Mr. Rouiller said, yet they appear to be relaxed — and they are almost casual in the moment when one is seen opening fire on a wounded police officer on the sidewalk.

Online, a spat was underway between Islamic State and Qaeda supporters, with each trying to claim credit for the attack. ISIS sympathizers pointed to a seven-minute video released in November and produced by the Islamic State’s official Al Hayat Media Center. It shows three French fighters burning their passports and imploring their countrymen to rise up. “There are weapons and cars available and targets ready to be hit,” says one of the French-speaking narrators.

“I don’t respect this head-to-head A.Q. and I.S. fan business over the French attack,” a self-described ISIS fighter going by the name Qaqa al-Baritani saidon Twitter, according to a transcript provided by SITE Intelligence, which tracks jihadist statements. “Even if A.Q. did it, we will praise it.”