Rates of new infections are increasing in all age groups, with people between the ages of 20 and 30 being most affected.
It is feared that this could be a sign of a second wave in the country, which has been completely destroyed by the pandemic.
France has the third highest number of deaths from Covid-19 in Europe, with more than 30,000 people dying from the virus.
Only the UK and Italy reported higher death rates.
Thousands of Scots are reportedly currently on vacation in France and the Home Office is “monitoring” the current situation.
All Scots returning to the country from France will be quarantined for 14 days if the list changes are passed.
The city of Toulouse has introduced new rules requiring face masks on its busiest streets, with Paris and a number of other cities to follow.
Wearing masks in enclosed public spaces has been compulsory throughout France since July 20 for children 11 and over.
The move comes as new quarantine measures have been introduced for travelers returning to Scotland from Belgium, Andorra and the Bahamas, starting at midnight.
Speaking to Sky News about the quarantine and whether France could be the next country to be added to the quarantine list, Chancellor Rishi Sunak told holidaymakers “there is always a risk of disruption ”during the pandemic.
He added: “It’s a delicate situation. What I can tell people is that we are in the middle of a global pandemic and that means there is always a risk of disruption to travel plans and people need to keep that in mind.
“It’s the right thing to do for us to keep everything under review at all times by talking to our scientists, our medical advisers, and if we have to act, as you have seen overnight, we don’t. will of course not hesitate to do so. that, and we’re doing it to protect people’s health.
France, Spain, Greece and Germany have all reported new spikes in infections, raising fears of a second increase in cases.
All three countries have seen marked increases in new coronavirus cases this week.