President Emmanuel Macron is counting on an accelerated vaccine booster programme to keep the virus in check.
Dr. Veran said he expected 22 to 23 million booster doses will have been administered by Christmas, up from 20 million as at Wednesday, Reuters reported.
"The objective is not to reduce the speed of the virus' spread because the variant is too contagious. The objective is to limit the risk of serious cases overwhelming hospitals," Dr. Veran told BFM TV. "This is why we are moving fast on booster shots."
Omicron has sparked a divided response in Europe.
Germany, Scotland, Ireland and the Netherlands are among countries that have reimposed partial or full lockdowns or other social distancing measures.
British Prime Minister Boris Johnson said he would not introduce new COVID-19 curbs in England before Christmas, but warned he might need to act afterwards.
France is reporting about 70,000 coronavirus infections a day as it battles a fifth wave of the epidemic.
The Omicron variant will be the dominant strain of the virus in France by early January, Dr. Veran said.
France has for months required a health pass for people to enter bars, restaurants, museums and other entertainment venues.
In recent days it has closed night clubs and cancelled New Year's Eve firework displays.
However, Dr. Veran said there were no plans at this stage for further restrictions or an extension of school holidays, though he cautioned nothing could be ruled out.
France registered 229 COVID-19 deaths on Tuesday, taking the country’s total death toll to 121,946.