penalised in the first two weeks of the nationwide quarantine, during which people can only go outside if it is deemed essential.
Those breaking the rules risk a fine of €135, which can increase to €200 if caught a second time, according to local media.
“Our goal is not to hand out fines,” Mr Castaner told TV channel La Chaine Info. “It is to make sure the French stay at home.”
France has been in lockdown since 17 March as authorities work to combat its coronavirus outbreak.
The lockdown – initially planned for two weeks – has now been extended until 15 April.
All public gatherings have been banned, and people are only allowed outside for a list of reasons, for example to buy food or medicine.
“At the end of these first ten days of confinement, it is clear that we are only at the beginning of the epidemic wave,” Edouard Philippe, the French prime minister, said last week.
“It has overwhelmed the east and is now arriving in the Ile-de-France and the Hauts de France.
Badly-hit areas of the country, such as the northeastern Grand Est region, have sent patients for treatment in other French regions and even abroad as authorities try and ease the pressure on overstretched hospitals.
On Wednesday, nearly 40 critically ill people are to travel from the Paris area to less overwhelmed regions by high-speed train, health officials said.
Military helicopters and planes have also been used to transfer patients since the start of the outbreak.
More than 52,000 people have been infected with coronavirus – which gives carriers flu-like symptoms and can turn into pneumonia – in France, with around 9,400 people who tested positive overcoming the virus.
The death toll stood at around 3,500 on Tuesday.