They also describe the sound of metallic banging from inside the aircraft. Both papers suggest the bangs could be the sound of the frantic captain attempting to break open the cockpit door with an axe, as Andreas Lubitz set the aircraft on to a collision course into the mountain.
German daily Bild and French magazine Paris Match said their reporters were shown the video after it was found on a memory chip that could have come from a mobile phone inside the aircraft.
Lieutenant Colonel Jean-Marc Menichini, a high-ranking official involved in the recovery operation, categorically denied that any mobile phone footage had been found by investigators at the site.
But Paris Match said the footage, thought to have been filmed from the rear of the plane, was found "among the wreckage by a source close to the investigation".
Bild, which described the scene as "chaotic, totally blurred and completely shaky", also insisted that the accuracy of the video "is beyond question".
According to Paris Match, cries of "My God" can be heard in several languages, before three metallic bangs ring out. They added that the footage captures the plane shaking heavily, before the screaming "intensifies".
Bild added that the aircraft appears to be touching a mountain, as more screams are heard. The camera then cuts out.
Both papers say the footage supports the idea that the passengers "knew what desperate situation they were in". It added that no individuals could be identified.
Although the two publications described the video in detail, neither posted the footage.
Bild said it was just "a few seconds" and that it is not clear whether a passenger or crew member had filmed it.
But mobile phone tester Dirk Lorenz told Bild: "It's very unlikely a mobile phone could have survived such an impact.
"However, a memory card can be very durable. Even if a mobile phone smashes into a thousand pieces the memory card can remain intact. For example when the impact was somewhat cushioned."
- Daily Mail