La vendeuse de la quincaillerie nous montre une échelle plus légère.

Vendeuse is the feminine form of vendeur (salesman / seller). Since the sentence is talking about a female shop assistant, French uses la vendeuse.

• le vendeur = the male seller
• la vendeuse = the female seller

French nouns for people often change form depending on gender.

Here, de la quincaillerie means from the hardware store or at the hardware store, depending on context.

Literally:

• de = of / from
• la quincaillerie = the hardware store

So la vendeuse de la quincaillerie is the saleswoman from the hardware store.

In French, de is often used to link a person to a place, business, or organization:

• le patron du restaurant = the owner of the restaurant
• la vendeuse de la boulangerie = the saleswoman from the bakery

Because quincaillerie is a feminine singular noun.

French uses:

• du = de + le for masculine singular nouns
• de la for feminine singular nouns
• de l’ before a vowel sound
• des for plural nouns

So:

• le magasin → du magasin
• la quincaillerie → de la quincaillerie

Since quincaillerie is feminine, de la is correct.

Because nous is an object pronoun, and object pronouns usually come before the conjugated verb in French.

Here, nous means to us:

• La vendeuse nous montre... = The saleswoman shows us...

This follows a very common French pattern:

• Il me parle. = He speaks to me.
• Elle nous donne un livre. = She gives us a book.
• Le professeur vous explique la règle. = The teacher explains the rule to you.

In English, pronouns like us usually come after the verb, but in French they often come before it.

Here, nous is an indirect object pronoun.

The full pattern is:

• montrer quelque chose à quelqu’un = to show something to someone

So:

• La vendeuse montre une échelle à nous is not the normal phrasing, but it helps reveal the structure.
• Standard French uses the pronoun before the verb: La vendeuse nous montre une échelle.

So:

• une échelle = the thing being shown → direct object
• nous = the people it is shown to → indirect object

Because the verb is conjugated here.

The infinitive is montrer = to show.
But the subject is la vendeuse, which is third person singular, so in the present tense:

• je montre
• tu montres
• il / elle / on montre
• nous montrons
• vous montrez
• ils / elles montrent

So la vendeuse montre = the saleswoman shows.

Because échelle is a feminine singular noun, so it takes the feminine singular indefinite article une.

• un = a/an for masculine singular nouns
• une = a/an for feminine singular nouns

So:

• un marteau = a hammer
• une échelle = a ladder

You usually just have to learn the gender of each noun as part of the word.

In French, most adjectives come after the noun.

So:

• une échelle légère = a light ladder
• une échelle plus légère = a lighter ladder

This is the normal position for many descriptive adjectives.
A small group of very common adjectives often come before the noun, but léger / légère usually comes after.

Because the adjective has to agree with the noun it describes.

The noun is échelle, which is feminine singular, so the adjective must also be feminine singular:

• masculine singular: léger
• feminine singular: légère

So:

• un sac léger = a light bag
• une échelle légère = a light ladder

The same agreement still applies with plus:

• un sac plus léger
• une échelle plus légère

Plus légère means lighter.

French often uses plus + adjective for the comparative:

• plus grand = bigger / taller
• plus cher = more expensive
• plus légère = lighter

If you want to say lighter than, French usually adds que:

• plus légère que cette autre échelle = lighter than that other ladder

But French does not always need to state the second item if the comparison is clear from context. So une échelle plus légère can simply mean a lighter ladder.

The accents are part of the spelling and pronunciation.

• é in échelle is pronounced like the ay sound in say (roughly speaking).
• è in légère shows a more open vowel sound.

These accents are not optional; they are part of the correct written form of the word.

For example:

• échelle
• légère

If you leave the accents out, the word is misspelled and sometimes harder to understand.

Yes, in practice quincaillerie often refers to a hardware store, especially in everyday use.

Depending on context, it can relate to:

• hardware goods
• metal fittings / household hardware
• the shop that sells them

In this sentence, la quincaillerie is naturally understood as the hardware store, because it is talking about a saleswoman working there.

Not in normal French.

With a full noun, you can say:

• La vendeuse montre une échelle aux clients. = The saleswoman shows a ladder to the customers.

But when the person is replaced by a pronoun like me, te, lui, nous, vous, leur, French normally uses the pronoun before the verb:

• La vendeuse nous montre une échelle.

So à nous is not the normal choice here unless you are stressing something in a special structure. For ordinary French, nous montre is the correct form.