Live updates: follow the latest news on Covid-19 variant Omicron
New cases totalled 368,149 on Tuesday, data from the Public Health Office showed, beating the previous record of just over 330,000 recorded last Wednesday.
The period is “unquestionably difficult, marked these last days by records of infections", French Health Minister Olivier Veran told the country’s Senate on Tuesday.
“The hospital system is subjected to a tremendous ordeal.”
There were 341 new deaths linked to Covid, taking the toll to 126,059. The steadily high numbers come as the debate around vaccinations heats up.
Politicians are discussing new legislation that would restrict access to restaurants, museums, trains and planes to people with full vaccination status.
French teachers are planning a strike on Thursday to protest against the measures in place to curb the spread in the virus in schools.
The government aims to enforce the new laws on January 15.