French President Emmanuel Macron said in a televised address to the nation on Monday that restrictions on public events would continue until mid-July.
France's round of the F1 championship is due to be held at the Circuit Paul Ricard, near Marseille, on 28 June.
F1 was unable to officially confirm the situation surrounding the race when contacted by BBC Sport.
Macron said France's lockdown would be extended until 11 May, after which creches and schools would progressively reopen, while bars, restaurants, and cinemas would stay shut. There would be no summer festivals "before mid-July".
The move seems to make it impossible to hold an event that was attended by 135,000 people last year.
The race would be the 10th grand prix to be called off at the start of a season that has been laid waste by the coronavirus crisis.