The 27-year-old West Ham player, who had pleaded guilty, was also banned by Thames Magistrates court in east London from owning a cat for five years.
Judge Susan Holdham described his actions as "shameful and reprehensible".
The video, where he was seen kicking and slapping his animal, was filmed on February 6 and shared on Snapchat by his little brother Yoan, 24, also a footballer.
During Kurt Zouma's court appearance on May 24, prosecutor Hazel Stevens said she was shot after cat damage caused a chair.
She had noted that since their publication there had been "an upsurge in people hitting cats and posting the images on various social networks".
The player's two cats have since been handed over to animal welfare society RSPCA, which had launched proceedings for Kurt and Yoan Zouma to be prosecuted under animal welfare legislation.
A protester disguised as a cat, on June 1, 2022, outside the London court which sentenced West Ham French defender Kurt Zouma to community service for abusing his animal Daniel LEAL AFP
The London club had not suspended their player and had even made him play a match the evening of the revelation of the affair, provoking a huge wave of protests.
The player was finally fined nearly 300,000 euros, the highest possible, imposed by his club and the sports equipment manufacturer Adidas had broken a sponsorship contract with him.
West Ham had assured that, according to the information available to the club, the cats "did not suffer any physical injury".
The club then assured that the financial penalty imposed on the player had been donated to animal protection associations.
© 2022 AFP