I did some home work and still have more to carry. Especially on the French Law. The difference would come from 1789 Universal Declaration of Human Rights that has the same position than the constitution and therefore in France, no treaty or law can go against.

Concerning the combatants, well…
The 3rd GC of 1949 defines the status of combatant in Art4. The treatment reserved to combatants is also valid for the persons that do not enter in the status of combatant by derogating to Art4 until a tribunal did status on their quality of combatant or on their quality of civilian (Art5). Even the civilian population taking arms without having all the qualitative distinctions of Art4 line 1 and 2. (Art4, line6)
I do not see where someone is not falling under GC.
The main issue with Taleb for example would be the uniform. This has been long ago accepted that uniform is not necessary. The main points of Art4 line 2 are: having a chain of command and carrying openly weapons. In war context, it is recognized as sufficient. Knowing that GC do not apply during riots. For the practice of terror, then the operations of British Air Forces during WWII on German cities would be used as a precedent justifying the use of terror in military operations. (not my cup of tea but it happened). Then the use of terror is part of the coutume of West. Does not say it makes it legal, just pointing the fact that the Art4 line2 d) can be challenged. And concerning terrorism should not.

The difference between banditry or riots and war will come from the intensity and the duration of the combats that will qualify the situation as war Cf :TPIY, Le procureur c/Dusco Tadic, Arrêt relatif à l'appel de la défense concernant l'exception préjudicielle d'incompétence, IT-94-1-A, 2 Octobre 1995, par.70.
On this, the US DoJ already lost a case to qualify a terrorist action as war action. (I do not have the reference right now but I believe it was about an attack on an Embassy in Peru). They tried to argue that a 4 hours combat (I am not so sure of the total duration but was less that a day) was a situation of war based on the element that the assailants used war weapons. The quality of the means, the weapons, was not sufficient to qualify the action as war action due to the duration of only 4 hours.
I believe that 2001 action in Afghanistan would be qualified as war. Especially if based on intensity and duration.
So once the quality of war is establish all combatants fall under the Geneva Convention. The main issue here would be does the USA recognize the TPIY as a legitimate legal structure.
USA did not ratify the Rome Status and are not recognizing the International Penal Court to not face such problem. But still the statement of TPIY is preceding 2001 and the Patriot Act and any administrative act from the Bush administration. Logically, it should apply or taken as argument to search for application.

Otherwise, prisoners fall under banditry and it falls under civilian law. And there you will fall under the Human Rights Convention and the Convention on Torture. Did the USA ratify the Universal Declaration of Human Rights? I believe yes. The one on torture, I am not so sure.

In both cases, this does not stop USA to arrest and jail dangerous terrorist. What it obliges USA to, is to give them trial and therefore an open scene to express their views. Then DoJ would have had to make the proof of their guiltiness. That may have been an issue but I doubt of it.

Also, taking the ICRC line, in March 2008, they made a statement that can be resumed to: as the ratification of GC is universal, all parties are entitled to respect GC. Basically all countries did ratify GC therefore all countries are bound to respect it and there is no room to declare that you will not respect it. (It took them some time to realize that every body did sign the paper… By the way)
ICRC legal line is much in accordance with French Law than USA law as they place the Universal Declaration of Human Rights from UN above all.
But there we will go to discuss Rawls theory of distribution of justice.

And finally, if a president of USA can by administrative act turn a treaty bounding USA, then can't he turn the constitution?
Then the constitution is no more protecting the people of America from dictatorship. As wrote Sinclair Lewis: it can't happen her. But did it not just happen here? Then the precedent created to protect civilian and soldiers from inhuman treatment is a problem.

Concerning the Mullah Omar rules. the question that comes to me is what version of Sharia they use and where does it fall in the hierarchy of law. Is the Sharia the supreme Law, even above the constitution? Is Sharia the reference of the constitution, as for Human Rights in French Law? Or is Sharia the referal for domestic laws? Concerning the GC, as ICRC does recognise Sharia as a coutume in war conduct, does Sharia have a higher rank in hierarchy for the Taleb or as for ICRC, is Sharia a contribution to GC?
Also, GC are not bound to a government but to a country. So as Afghanistan did sign and ratify GC in the past, then Taleb have to apply it. But do they recognise treaty and conventions that were ratify before they came in power?