France's government is demanding reassurances on safety from England and Ireland before allowing its national side to visit those countries during the Six Nations.
Only the Championship's opening fixture against Italy in Rome on February 6 has been approved by Sports Minister Roxana Maracineanu.
The French authorities have concerns over the soaring number of Covid-19 cases in the UK and Ireland and have already barred their clubs from taking part in European competition this month.
"There has to be proof that the other nations' virus framework respects the same requirements in terms of precaution. We expect the same thing from the other teams."
The Women's Six Nations and Under-20s competitions, which are traditionally run in tandem with the men's, are set to be postponed until April and May with official confirmation of their delay expected on Wednesday.