Several thousand people gathered at the famous landmark in the French capital after the north African country's victory against Ivory Coast, which sent the team into the semi-final of the tournament.
But as fans celebrated, a group smashed their way into two stores nearby, including a motorcycle shop, an AFP journalist said.
Dozens of people looted the stores, taking helmets, gloves and also motorcycles.
Police used tear gas to disperse the crowds and at least one person was arrested, the AFP journalist added.
Football fans traditionally gather at the Champs-Elysees to celebrate key football victories.
Tear gas was also used to control crowds of Algerian supporters who had gathered at the Old Port in Marseille to mark the win.