The match was due to take place in Paris on Sunday but was called off after another French player - the 11th - tested positive for Covid-19.
It was suggested earlier in the week that the game could be played next weekend which is not a scheduled Six Nations window.
Townsend, the Scotland coach, was left worrying that if it was rearranged for the Championship’s fallow week he would be denied the services of his English-based players, including captain Stuart Hogg, Jonny Gray, James Lang and Chris Harris, as Premiership sides would be under no obligation to release their players.
Given the scale of the outbreak in the French squad, however, next weekend now appears an unlikely option.
Discussions between the two nations plus Six Nations chiefs and TV broadcasters on a rearranged date are ongoing and, while reports in France now say July is being considered, this is unlikely to find favour with Murrayfield as it would clash with Lions matches.
Townsend said: “While we fully accept the decision of the Testing Oversight Group to recommend postponing our match against France on medical grounds, it is disappointing not to be able to play this fixture on Sunday.
“We have had a good week with our players, who were focussed and ready to represent their country in Paris and continue our progress in this year’s Guinness Six Nations.
“Throughout this tournament, and the previous Autumn Nations Cup, we have worked hard to maintain strict Covid protocols which have enabled us to select our strongest possible teams for these important international fixtures.
“We will wait to see what options are available to play this match against France, but it remains our position that we want to have all our eligible players available to us for that fixture, so we can compete to the level we would have done this weekend.
“We wish all the French players and staff affected by Covid well in their recovery and look forward to playing them at a future date.”
The game has been in doubt all week as Fabien Galthie’s squad saw player after player test positive, with the head coach himself among a number of backroom staff to self-isolate. Captain Charles Ollivon and 2020 player of the championship Antoine Dupont were among those to contract the virus.
Tournament organisers responded by ordering the French squad to undergo daily testing – before announcing on Wednesday that the game would go ahead as planned following a full sweep of negative results.
But less than 24 hours later they have been forced to postpone the Stade de France clash, with the entire Les Bleus squad placed into quarantine after the French Rugby Federation reported yet another player had contracted the virus.
The Six Nations said in a statement: “The Six Nations Testing Oversight Group met today to review the situation in the French camp.
“They unanimously recommended the postponement of the France v Scotland match. This will be ratified later today by the Six Nations council.
“We will be working on the rescheduling of this fixture and will communicate the date in due course.”