Government spokesman Gabriel Attal told reporters a mandatory quarantine would be announced “in the coming hours”.
Britain recorded 3,424 cases of the B1617.2 mutation first found in India in the last seven days – an increase of 2,111 on the previous week.
England’s chief medical officer Professor Chris Whitty has said the Indian variant is “more transmittable” than the Kent one responsible for the UK’s deadly wave of coronavirus infections this winter.
He said: “We expect, over time, this variant to overtake and come to dominate in the UK.”
A study earlier this week found that two injections of the Pfizer or AstraZeneca vaccines offered a similar level of protection against symptomatic disease from the Indian variant as for the Kent one.
But protection after a first dose was lower in the Indian variant compared to Kent version, with 33 per cent and 50 per cent effectiveness respectively.
France currently requires travellers from 16 countries including Brazil, India, Argentina and Turkey, to undergo an obligatory 10 days of self-isolation either at home or at an approved address.
Travellers have the right to go out only two hours a day and face a €1,500 fine in the event of non-compliance.
France, Germany and Austria are all on England’s “amber” list, meaning that the government advises against travel there and passengers must quarantine upon return.
However, France had planned to allow fully vaccinated travellers from the UK - or those who had tested negative - to visit from June 9.
Spain, another amber country, has already reopened to UK tourists.
Last week, the EU agreed on a pass to allow travel across the bloc’s 27 countries for all those who have been fully vaccinated with an approved vaccine, recently tested negative or recovered from an infection.
That is expected to launch by July.