The White House also plans to announce stricter testing for international visitors.
French government adviser Jean-Francois Delfraissy told BFM television the "true enemy" for now was still the Delta variant, spreading in a fifth wave.
"We should see a progressive rise of the Omicron variant, which will take over from Delta," possibly by the end of January, he said.
"Christmas is not at risk if the population and decision-makers are all very cautious," he said, reiterating that social distancing and a third, booster shot of vaccines were key.
The French Omicron infection followed a case found in the French Indian Ocean island of La Reunion last month.
Airlines in the United States were told to hand over the names of passengers arriving from parts of southern Africa, a U.S. Centers for Disease Control and Prevention letter seen by Reuters showed.
Much remains unknown about Omicron, which was first found on Nov. 8 in South Africa and has spread to at least two dozen countries, just as parts of Europe were suffering a surge in infections of the better-known Delta variant as winter sets in.
Top U.S. infectious disease expert Anthony Fauci on Wednesday said it could take two weeks or more to gain insight into how easily the variant spreads, the severity of the illness that it causes and whether it can evade currently available vaccines.
South Africa's National Institute for Communicable Diseases (NICD) said early epidemiological data suggested Omicron was able to evade some immunity, but existing vaccines should still protect against severe disease and death.
World Health Organization (WHO) epidemiologist Maria van Kerkhove told a briefing that data should be available "within days" on Omicron's contagiousness.
BioNTech's CEO said the vaccine it makes in a partnership with Pfizer was likely to offer strong protection against severe disease from Omicron.
And GlaxoSmithKline said that a lab analysis of the antibody-based COVID-19 therapy it is developing with U.S. partner Vir had shown the drug is effective against the Omicron variant.
This contrasts with Regeneron's study of its COVID-19 antibody drug, which it said could be less effective against Omicron, adding to fears about the efficacy of existing treatments. Moderna's top boss raised similar concerns about the company's vaccine.
Indications suggesting Omicron may be markedly more contagious than previous variants have rattled financial markets, fearful that new restrictions could choke a tentative recovery from the economic impact of the pandemic.
European stock indexes opened lower on Thursday, reversing gains from the previous session as a lack of information about Omicron left markets volatile.
Bank of Japan board member Hitoshi Suzuki said Japan's economic recovery may miss expectations if the spread of the Omicron variant limits consumption, or supply bottlenecks persist.
About 56 countries were reportedly implementing travel measures to guard against Omicron as of Nov. 28, the WHO said.
The United States has barred nearly all foreigners who have been in one of eight southern African countries.
Japan reversed a ban on new inbound flight reservations, revealing confusion between government agencies and the public over the country's COVID strategy.
The European Union brought forward the start of its vaccine rollout for 5-to-11-year-olds to Dec. 13, as the president of the European Union's executive body said there was a "race against time" to stave off the new variant.
Britain and the United States have both expanded their booster programmes in response to the new variant, although the WHO says wealthy countries should instead share more vaccines with vulnerable people in poorer countries where variants are most likely to emerge as long as inoculation rates are low.
Dutch health authorities meanwhile said that more than half the passengers who have been in quarantine since testing positive for COVID-19 after flying from South Africa on Nov. 26 will be allowed to leave on Thursday after testing negative.
And Israel's Supreme Court rejected a petition by rights groups seeking to repeal temporary measures allowing the domestic intelligence agency to use mobile phone tracing to curb the spread of the new COVID-19 variant.
(Reporting by Reuters bureaux; Writing Stephen Coates, Nick Macfie and Ingrid Melander; Editing by Simon Cameron-Moore and Barbara Lewis) ((email@example.com))