Le droit de rétractation permet ce retour.

Because le droit de rétractation is the subject of the sentence.

• le droit = the right
• de rétractation = of withdrawal / cancellation

So the whole noun phrase le droit de rétractation means the right to cancel/withdraw. In legal or consumer contexts, this refers to the buyer’s legal right to change their mind within a certain period.

Here, rétractation refers to withdrawing from an agreement or purchase. It is a fairly formal/legal noun.

It comes from the verb se rétracter, which means to withdraw what one said, to back out, or in legal/consumer language, to cancel by exercising a withdrawal right.

So in this sentence, droit de rétractation is a fixed legal expression, often used in online shopping and contract law.

Because droit de + noun is a very common French structure.

Examples:

• le droit de vote = the right to vote
• le droit de réponse = the right of reply
• le droit de rétractation = the right of withdrawal

You do not say du rétractation because:

1. rétractation is feminine, so du would already be wrong grammatically.
2. More importantly, this expression uses de in a fixed pattern: droit de + noun.

Because permet is the conjugated form of the verb permettre in the present tense.

The subject is Le droit de rétractation, which is singular, so the verb must also be singular:

• je permets
• tu permets
• il/elle/on permet
• nous permettons
• vous permettez
• ils/elles permettent

So:

• Le droit de rétractation permet... = The right of withdrawal allows...

Ce retour means this return.

• ce = this
• retour = return

In context, retour usually means the act of returning an item. So ce retour refers to a specific return, probably one already mentioned in the surrounding text.

Because retour is a masculine singular noun that begins with a consonant sound.

French uses:

• ce before masculine singular nouns beginning with a consonant sound
  
  • ce livre
  • ce retour
• cet before masculine singular nouns beginning with a vowel or mute h
  
  • cet article
  • cet achat
• cette for feminine singular nouns
  
  • cette commande

So retour takes ce.

Because permettre can take a direct object.

Here, ce retour is the thing being allowed:

• Le droit de rétractation permet ce retour.
• literally: The right of withdrawal allows this return.

French also very often uses permettre de + infinitive:

• Le droit de rétractation permet de retourner l’article.
• The right of withdrawal allows you to return the item.

Both patterns are possible:

• permettre + noun
• permettre de + infinitive

Yes, it is understandable and grammatically correct, especially in formal or legal context. However, depending on the context, French might more naturally say things like:

• Le droit de rétractation permet ce type de retour.
• Le droit de rétractation autorise ce retour.
• Ce retour est possible grâce au droit de rétractation.

So the original sentence is fine, but it sounds somewhat formal and possibly administrative.

Both can often be translated as to allow, but there is a slight nuance.

• permettre = to make possible, to allow
• autoriser = to authorize, to give official permission for

In this sentence:

• Le droit de rétractation permet ce retour suggests that the legal right makes the return possible.
• Le droit de rétractation autorise ce retour sounds a bit more explicitly like official permission.

In legal or policy language, both can work, but permettre is a little broader.

Because grammatical gender in French is a property of the noun itself, and retour happens to be masculine: le retour.

This is something learners usually have to memorize with each noun:

• le retour = the return
• la rétractation = the withdrawal/cancellation

That is why the sentence has:

• Le droit
• la rétractation
• ce retour

A simple pronunciation guide is:

Le droit de rétractation permet ce retour.
luh drwah duh ray-trak-ta-syon pair-may suh ruh-toor

A few points:

• droit sounds roughly like drwah
• rétractation ends with -syon
• permet ends with an ay sound
• retour has the French r, which is pronounced in the throat

There is no strong stress on one word like in English; French rhythm is more even.

Yes, absolutely. That is a very natural alternative.

Compare:

• Le droit de rétractation permet ce retour.
  • focuses on this return
• Le droit de rétractation permet de retourner l’article.
  • focuses on the action of returning the item

The second version may feel clearer to many learners because permettre de + infinitive is a very common and transparent pattern in French.