Officials say the police will patrol the Stade de France stadium as well as the Fan Zone near the Eiffel Tower and the Champs Elysees boulevard.
But there will be no victory parade if France win, the officials warned.
Police and the army have been patrolling Paris since last November`s attacks in which 130 people died.
Jihadist gunmen and suicide bombers attacked a number of venues, including the Stade de France.
`High standard`
French officials say about 1,900 police officers will patrol the Fan Zone, while another 3,400 will be deployed at the Champs Elysees - some of them will be moved from the stadium, just north of Paris, after the final kicks off at 21:00 local time (19:00 GMT).
"We have the extremely favourable ratio of one officer for fewer than 50 spectators. So it is an extremely high standard," said Mathias Vicherat, the Paris mayor`s chief of staff.
But officials have said that there will be no victory parade on the Champs Elysees in the event of a French win because of security concerns.
More than one million people celebrated France`s 1998 World Cup victory there.
Police and security forces have already successfully patrolled 11 matches played so far at the Stade de France and at another Paris stadium, the Parc des Princes.
However, the authorities have been criticised for their inability to prevent clashes between rival fans at a stadium in Marseille and also on the streets of the southern city.
Euro 2016: France beefs up security ahead of final match
10 July 2016
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More than 5,000 French police will be deployed at key venues in and around Paris ahead of the Euro 2016 football final between France and Portugal.
