".When a wise man argues at length with a fool, it becomes difficult to distinguish whoisthe fool"
Should I use "who the fool is"?
....who the fool is - the best choice and the correct word order in an English sentence of this type.
If it were an interrogative sentence, then the word order should be the one written in your sentence.
I am going to disagree - as a sentence it is fine, if somewhat "poetic" or rhetorical.
In fact, if you say both alternatives aloud (within the sentence), you will very likely find that "who is the fool" sounds better.
I agree that 'who is the fool" sounds better, especially for foreign learners, which is my case, as well ; but, I understand that, in an exam, [say, FCE], one is supposed to know the correct order in English sentences. Moreover, if students who take a Baccalaureat examination [written exam] write the answer "who is the fool", it [the answer] will be marked as wrong.