The Premier League new-boys had agreed a £250,000 transfer fee to sign Situ from Lens, as well as a loan deal for Fulham defender Halliche, on transfer deadline day.
However, manager Brendan Rodgers has been unable to field the duo whilst awaiting the green light from the world game's governing body and, due to minor delays in processing the transfers, the south Wales club have now been informed they will not be granted international clearance for either defender.
FIFA's decision comes despite Swansea having the full backing of the Premier League, the Football Association of Wales, the FA, the French Football Federation and the Professional Footballers Association.
Swansea will await official written confirmation from FIFA before considering whether to appeal.
A Swansea statement read: "Swansea City is disappointed with FIFA's decision and are currently pursuing other options to strengthen the squad.
"The club will not be making any other comment at this stage until full written clarification is received from FIFA.
FIFA's decision not to give international clearance for the two defenders is a big blow for Rodgers, who returned to work on Thursday following the death of his father, as he is already short of defensive options.
Alan Tate (broken leg) and on-loan defender Steven Caulker (knee) are sidelined, with the latter possibly in need of an operation after damaging knee cartilage against Arsenal.
And midfielder Kemy Agustien, who Rodgers had considered as potential centre-half cover, is likely to be out for six weeks with the hamstring injury he suffered in the defeat at the Emirates.
But skipper Garry Monk, who may be required against West Brom on Saturday, is returning from a foot problem.
Rodgers said: "It's incredible really. When you have the Premier League, the FA, the French Federation, everyone sees there is innocence if there was maybe something that did not go through.
"But FIFA are saying it is not valid at this point, but until we get written evidence we will have to wait and see. But if that is to be the case then it is obviously very disappointing."
Of his injury problems the Northern Irishman added: "Since I have come here we have had a wonderful run in terms of injuries, the conditioning of the players has been superb. But we are running up bad luck on and off the field.
"On the field our levels of performance have been high but we haven't had the luck to get a goal.
"Off the field we have lost a number of players. We only have one soft tissue injury, in terms of a hamstring with Kemy from last Saturday.
"Other than that we have had a blow with Craig Beattie and his ankle, he is likely to be out for around six weeks, and Andrea Orlandi has an ongoing problem with his knee.
"Steven Caulker has been magnificent for us but he will go back to Tottenham, we have had look at it at our end and there is a possibility he will have a small operation on Saturday.
"He will go back to Tottenham for their medics to have a look at it as well and we should know the outcome on Friday."