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Tournament organisers say they are considering "all possible fixture permutations" following opening-round postponements in the European Champions Cup and Challenge Cup competitions.
Four-time European title holders Toulouse were the only French team in action on the weekend, losing 32-7 against Saracens at Allianz Park.
Games scheduled to be hosted by Racing 92, Oyonnax, Bordeaux-Begles and Toulon were all postponed by European Professional Club Rugby and French domestic rugby chiefs Ligue Nationale de Rugby following the Paris atrocities that left 129 dead.
Eight matches across both tournaments are due to take place on French soil later this week, including Paris-based Stade Francais hosting Munster next Sunday.
"Following last weekend's round one postponements in the Champions Cup and Challenge Cup, EPCR is currently working in conjunction with the LNR, PRL (Premiership Rugby) and the PRO12, as well as the relevant clubs, to consider all possible fixture permutations with the aim of coming up with a workable solution as to how the matches can be rescheduled in an already crowded rugby calendar," an EPCR spokesman told Press Association Sport.
"EPCR and the three leagues hope to be in a position to make an announcement as soon as possible."
Stade Francais apart, matches are listed to take place between next Thursday and Sunday in La Rochelle, Agen, Montpellier, Toulouse, Castres, Grenoble and Clermont-Ferrand.
Gloucester are due at La Rochelle next Thursday, with London Irish visiting Grenoble two days later. Both games are Challenge Cup fixtures, in addition to Edinburgh visiting Agen and Newport Gwent Dragons being away to Castres. The Ospreys, meanwhile, face a Champions Cup away game against Clermont Auvergne next Sunday.
Bath are currently the only English club affected in terms of rescheduling after the Pool Five appointment with Champions Cup holders Toulon at Stade Felix-Mayol on Sunday was postponed.
But the west country club do not have a free weekend until early April, and that is only if they fail to make the Champions Cup quarter-finals.
Bath chairman Bruce Craig, who is one of two English representatives on the EPCR board, said he thinks finding a suitable rearrangement date will not be possible.
"It is very clear to me that the Toulon match can't happen," Craig told the Daily Telegraph on Monday.
"The midweek option is not an option to my mind, as that would be to the detriment of player welfare as well as the integrity of two competitions, an important Champions Cup game being squeezed in with all the attendant travel issues between two Premiership weekends.
"There is no way we should be letting that happen. You can't play three high-profile games in a week.
"In the wider context of what has happened in Paris, this is not a serious matter, of course it isn't. And I do understand why the decision was taken.
"But from a rugby point of view, and from the point of view of the competition, this is an issue of significant consequence. There is no place to fit it in."
Mourad Boudjellal, the president of Toulon, has suggested the postponed game against Bath could take place during the RBS 6 Nations.
The knockout stages of the Champions Cup are not set to take place until early April while the Six Nations kicks off on February 6.
Boudjellal did concede any rearrangement would prove complicated, highlighting the difficulty in potentially releasing international players to play for their clubs, but he was willing to find a solution.
"Playing on Wednesday isn't possible," he told French sports daily L'Equipe.
"I can only see one solution... It would mean that the (national team) coaches would have to accept not being able to call up international players of Bath or Toulon in order for us to be able to play the match during a matchday of the Six Nations."