There have been security concerns across Europe since the attacks in Paris, which killed 130 people.
However, France's sports minister Patrick Kanner said fan zones would "tell the French people and foreigners that everything is under control".
Elsewhere, Russia says security at the 2018 World Cup will be strengthened.
"We discussed the problems of security in detail," said Russia's sports minister Vitaly Mutko after a meeting with Fifa inspectors.
The minister said that security at the World Cup construction sites had already been toughened up, and the fan zones at the 2017 Confederation Cup and the World Cup will be at the centre of the security forces' attention.
Euro 2016 will be played from 10 June to 10 July in 10 French cities.
In Paris, the fan zone is expected to have a 120,000 capacity and will be situated on the Champs de Mars, below the Eiffel Tower.
Euro 2016 organisers are hopeful supporters will be allowed to watch matches on big screens in public areas of France next summer.