The video -- which was believed to be filmed by Zouma's brother and posted to Snapchat over the weekend -- is disturbing ... and shows the 27-year-old picking up a cat and then kicking it across the floor.

Later in the footage, which was obtained and published by The Sun, Zouma can be seen appearing to throw things at a cat. Finally, toward the end of the clip, video shows Zouma slapping one of the animals in the face.

Zouma released an apology this week following an outpouring of criticism ... saying, "There are no excuses for my behaviour, which I sincerely regret."

"I also want to say how deeply sorry I am to anyone who was upset by the video," he added. "I would like to assure everyone that our two cats are perfectly fine and healthy. They are loved and cherished by our entire family, and this behaviour was an isolated incident that will not happen again.”

Zouma's West Ham team also issued a statement condemning Zouma ... though it controversially decided to allow Zouma to play in its game Tuesday despite the player's actions.

Reporters on the scene say the footballer is being loudly boo'ed every time he touches the ball.

Cops, meanwhile, have told multiple outlets they are aware of the video.