The zone, where crowds can watch games on giant outdoor screens, was closed after reaching its maximum capacity of 90,000 at around 7 p.m. (1700 GMT), police said.
During the second half of the match, police used water cannons to keep people from trying to break in again while firefighters extinguished scooters and a car set ablaze just outside the fan zone.
"The fire is being handled," a police source said.
Police called on drivers to steer clear of the Eiffel Tower and nearby Trocadero area as some people were blocking traffic and intercepting cars.
The match between Portugal and France began at 1900 GMT and by 2120 GMT, the score was 1-0 for Portugal.
(Reporting by Bate Felix and Chine Labbe; writing by Astrid Wendlandt; editing by Gareth Jones and David Gregorio)
