Football exists in it's own legal eco system which has a hierarchy of clubs, national federations, continental federations and ultimately FIFA. There is a dispute resolution process with the ultimate arbiter being CAS. Providing all parties operate and co-operate within that eco system there is no need for any other authority to be involved unless the activity concerned could be deemed as criminal e.g. match fixing.
As such football has it's own unique set of rules which are transnational. This does not mean that clubs aren't subject to the jurisdiction of the courts in the country they operate within but unless someone seeks redress through those courts the football rule book stands. However as soon as there is a challenge particularly in Europe (and that does include non-EU countries) the rules are very quickly exposed as being unfair to employees, e.g. Bosman and pretty much every case that has gone to an employment tribunal in the UK.
If the football authorities want to maintain legal hegemony over the game they cannot afford not to iron out a settlement within it's own system. Finding Diarra liable for the transfer fee in this dispute was madness and would obviously be challenged in a real world court. The problem is not the specifics of the case but the broader implications of restraint of trade and freedom of movement, this is where the genie escapes from the bottle.
FIFA are belatedly amending their rule book which addresses the issue of players whose contracts are terminated being held liable for any transfer fee associated with the contract i.e. fixing the specifics of the case. This is unfortunately closing the stable door after the horse has bolted and this particular horse is now grazing in very green pastures and is disinclined to return to the stable.
The problem for the football authorities is that courts have this rather annoying habit of looking at legal principle and not viewing an issue through the uniquely Alice in Wonderland lens of football. The courts have decided that footballers are employees like the rest of us and are able to change employers without a transfer fee over and above the remedy for breach of contract. The court acknowledge the need to ensure continuity of squads during competitions but was clear the current rules go way beyond that.
FIFA are confident that it hasn't blown up their rule book. Frankly I wouldn't set a whole lot of store by that as they are the same bunch of idiots that didn't settle the case in the first place.
I have come to this view based on wading through legal writers take on the case rather than that of the sports journalists.