Following the spread of the SARS-CoV-2 B.1.1.7 variant, social distancing was strengthened in France in January 2021. Using a two-strain mathematical model calibrated on genomic surveillance, we estimated that curfew measures allowed hospitalisations to plateau by decreasing transmission of the historical strains while B.1.1.7 continued to grow. School holidays appear to have further slowed down progression in February. Without progressively strengthened social distancing, a rapid surge of hospitalisations is expected, despite the foreseen increase in vaccination rhythm.