La vendeuse du rayon de bricolage me conseille un petit coffret avec des vis et des clous.

Du is the contraction of de + le. In this sentence, la vendeuse du rayon de bricolage identifies the saleswoman as the one from the DIY/hardware department.

This is very common in French:

• le vendeur du magasin
• la responsable du service client
• le chef du restaurant

So du rayon links the person to a specific section or department.

After a noun like rayon, French often uses de + noun to name the type or category of that section:

• un rayon de bricolage
• un magasin de sport
• une salle de classe

Here, bricolage is being used as a category name, so French uses de without an article. It is similar to saying the hardware/DIY section rather than the section of the DIY.

Vendeuse is the feminine form, used for a female salesperson. Vendeur is the masculine form.

So:

• le vendeur = a male salesperson
• la vendeuse = a female salesperson

The article also changes to match:

• le vendeur
• la vendeuse

In French, object pronouns usually come before the conjugated verb. So me conseille follows the normal French pronoun order.

Compare:

• Elle me conseille...
• Il lui parle
• Nous vous attendons

English puts this idea after the verb much more often, but French puts the pronoun before it.

Here, me is the pronoun referring to the person receiving the recommendation. In natural English, this is often expressed as to me.

So the structure is:

• the saleswoman = the person doing the action
• me = the person affected by the action
• un petit coffret = the thing being recommended

This is a very common pattern with verbs involving communication, advice, or giving.

Conseiller can be used with both a person and a thing. In sentences like this, French can express:

• who is being advised
• what is being recommended

Common patterns include:

• conseiller quelque chose à quelqu’un
• conseiller à quelqu’un de + infinitive

In your sentence, the person is shown by me, and the recommended item is un petit coffret.

French adjectives usually come after the noun, but some very common short adjectives often come before it. Petit is one of those adjectives.

So French says:

• un petit coffret
• une grande maison
• un jeune homme

This is part of the common adjective pattern often remembered with the BAGS group: Beauty, Age, Goodness, Size.

Because coffret is a masculine singular noun. That means both the article and the adjective must agree with it:

• un for masculine singular
• petit for masculine singular

If the noun were feminine, you would get forms like une petite...

Des is the normal indefinite article for plural countable nouns. Here, the sentence is talking about some screws and some nails, so French uses:

• des vis
• des clous

This is the ordinary form in an affirmative sentence. French often changes des to de in special situations, such as after negation, but not here.

Because avec does not remove the article. After avec, French normally keeps the article that the noun needs.

So:

• avec des vis
• avec un marteau
• avec la notice

The preposition avec simply means with; it does not change the article pattern.

In shopping French, rayon is commonly used for a department, section, or aisle of a store. It is a very common store-related noun.

For example:

• le rayon fruits et légumes
• le rayon bricolage
• le rayon jouets

So la vendeuse du rayon de bricolage is a very natural retail expression.

Yes, but it changes the focus a little.

• la vendeuse du rayon de bricolage = the saleswoman from that department
• la vendeuse dans le rayon de bricolage = the saleswoman in that department

The original sentence sounds more like identifying her job or department. The version with dans sounds more like describing where she is physically located.

Yes, a few common ones:

• Final letters are often silent: rayon, clous
• vendeuse ends with a pronounced z sound
• conseille sounds roughly like kon-say
• un has a nasal vowel, not a strong n sound
• et usually blocks liaison, so des vis et des clous does not create a liaison across et

A careful learner should especially notice the rhythm of me conseille un petit coffret, where French links words smoothly even when many final consonants are not pronounced.