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It comes as the country’s daily case tally topped 100,000 for the first time on Saturday – a rise of 78 per cent on last week.
From Monday, all public gatherings will be limited to 2,000 people for indoor events, and to 5,000 people for outdoor events.
The government has also banned eating and drinking on public transport, while anyone visiting a bar and restaurant will only be able to eat or drink while sitting down.
Mr Castex said working from home would also be mandatory for at least three days a week. Mask wearing will also be mandatory outdoors in city centres.
The measures will last for three weeks, unless a change in the data forces ministers to take further action.
France’s Covid incidence rate - the number of infections per 100,000 people per week - is now well over 700 and at a record level since the start of the pandemic, forcing his cabinet to take new measures.
"I know that it feels like a film without ending, but a year ago we started our vaccination campaign and now we are one of the best vaccinated and best protected people in the world," Mr Castex told a news conference following a cabinet meeting.
The government will also narrow the period until people are eligible for a booster shot to three months from four following their second jab in a bid to speed up the booster campaign.
France recorded a record high of 104,611 Covid infections on Saturday, breaking the 100,000 threshold for the first time since the pandemic began as the omicron variant continued its rapid spread.