The resort city of Cannes on the Côte d'Azur has trialled the monitoring software, installed at outdoor markets and on buses.
It is not clear how many other cities will adopt this digital surveillance.
French firm Datakalab says its software does not violate EU data privacy law.
"No image is stored or transmitted, ensuring that personal information is protected," Datakalab said, announcing its collaboration with Cannes city hall, ahead of the 11 May relaxation of France's tough lockdown.
Many artificial intelligence (AI) innovations are being adopted worldwide in the rush to stop the spread of Covid-19, and use of these tools, under emergency laws, has raised the alarm about possible invasions of privacy.
The French surveillance system does include an automatic alert to city authorities and police where breaches of the mask and distancing rules are spotted.
But Datakalab, a startup launched in 2017, insists that it is "not facial recognition", as the system does not store identifying data. That sets it apart from the kind of hi-tech surveillance common in China.
Datakalab says its algorithms can be incorporated into existing surveillance systems in other public spaces, such as hospitals, stations, airports and shopping centres.
France has suffered one of the highest Covid-19 death rates in Europe, along with the UK, Italy and Spain. The French death toll - which includes deaths in care homes - now stands at 24,895.
From 11 May face masks will be compulsory in France on public transport and in secondary schools.
Shops and markets will also have the right to ask shoppers to wear masks, and should ensure they remain a metre (3ft) apart, the French government says.