I am reading a beginners book to learn French. Somewhere in the book there is this sentence:
Tu n’as aucun accent !
You have no accent!
My question is, shouldn't it be "Tu n'as pas aucun accent !" instead?
ne + pas is the most standard negation indeed, but pas can be replaced with another word. For instance, you have ne + aucun, ne + jamais (Je ne suis jamais allé à Disney Studios.), ne + personne (Heureusement, il n'a blessé personne.), …
This is just incorrect. An English approximation of this would be "You don't have no accent!" It might be the contrary of your meaning in an inelegant way, or just a plain mistake (though I understand the question).
As the OP remarked, this English form, though not being taught when learning English as a foreign language, exists in informal speech in some parts of the US. The French form, though, is incorrect everywhere as far as I am aware.
These are just examples, far from an exhaustive list. Please note they are not rules and may depend on context
Normal use no longer allows pas/point with aucun, nul, jamais, rien, personne or guère to express a single negation. A reason for that is that such words have gained a negation meaning over time and cancel themselves out when used in such combinations (ce n'est pas rien/ne... pas... que). It is even more intricate as in some cases you can have such one negation being used positively in a negative context (viens-tu pas demander asile ? (Hugo)) and further cases where it is considered more acceptable (Il ne recommandait pas de tuer personne au nom de cette suprématie (Henriot)); the latter usually involving the use of a preposition or the second auxiliary being used as a complement. This should also be distinguished from cases where two negations are close but apply to different verbs (je ne vois pas cependant qu'aucun ait blâmé... (Brunot)) and therefore don't constitute a double negation.
But those restrictions may not apply to popular speech (je n'ai pas rien trouvé, attested) and therefore you may hear something such as the "tu n'as pas aucun accent" you mention, albeit not in a beginner's book geared at learners. You may also find it in more classical work :
Je n'ai pas besoin d'aucune preuve (Claudel)
Cette collection comme aucun prince n'en possède pas à l'heure actuelle (Proust)
There used to be a time when you could have combinations which are no longer normally allowed; the ne element carried over the whole negation and what followed had basically no impact over it : L'i de cette particule [=si] ne se mange point devant aucune des cinq voyelles (Vaugelas).1
1. All examples and content adapted from Le bon usage (Grevisse et Goosse, ed. Duculot) §§ 1019, 1021.