Heineken Champions Cup and EPCR Challenge Cup pool-stage matches in rounds three and four will go ahead.
A statement from EPCR said: "Following dialogue with the leagues and unions, EPCR has been informed that exemptions for what is termed the "pursuit of an economic activity" which have been put in place by the French government will apply to clubs and match officials who are travelling between France and the UK.
"Further information will also be sought from the French authorities regarding possible new conditions which may be applicable to travel between France and the UK."
Travel restrictions imposed in France, due to Covid-19, had caused multiple postponements in round two.
An exemption from the French government will now allow teams to travel between Britain and France.
Leinster's cancelled game against Montpellier was awarded 28-0 to the French side.
EPCR insists the tournament can be finished successfully and are planning to reschedule postponed games, likely in April.