The peak in the third wave of Covid-19 in France "appears to be behind us", Prime Minister Jean Castex said on Thursday.
Mr Castex said travel restrictions would be relaxed from early May.
He said there had been a "genuine fall in the circulation of the virus over the last 10 days".
A restriction that bars people from travelling more than 10 kilometres from their homes will be dropped on May 3, Mr Castex said.
France is under its third lockdown to stem the spread of the virus but this time it has been considerably more relaxed, with outdoor activities encouraged to promote mental health.
But most non-essential shops have been closed, along with cafes, restaurants and cultural venues.
Owners in many sectors are putting pressure on the government to reopen after months of closure.
Mr Castex said "shops, certain cultural and sporting activities and the cafe terraces" could reopen "around mid-May", depending on how the outbreak developed.
He said the government could also start to reopen businesses on a regional basis, beginning with areas that have fewer cases.
A nationwide 7pm curfew would remain in place until further notice, Mr Castex said.
While the measure will be reviewed in mid-May, he did not say when it would be relaxed.
There were 5,981 people with coronavirus in intensive care units in France on Thursday, official data showed, after flattening out below 6,000 in recent days.
A total of 102,164 people have died in France from the pandemic but after a slow start the vaccination campaign is gaining pace, with more than 13 million people now given at least a first dose.
Health Minister Olivier Veran said that from Saturday, France would begin offering the Johnson & Johnson single-shot vaccine to people aged 55 and over.
It will be the fourth vaccine offered by France after those developed by Pfizer-BioNTech, Moderna and AstraZeneca.
Europe's medicine regulator said on Tuesday that blood clots should be listed as a "very rare" side-effect of the Johnson & Johnson vaccine, but that the benefits of the shot outweighed the risks.
French Interior Minister Gerald Darmanin, meanwhile, said that to keep Covid-19 variants out of the country, all passengers arriving from Argentina, Brazil, Chile, India and South Africa would need to enter quarantine at their place of residence for 10 days.
Their isolation will be monitored by police.