Nous avons acheté une petite pastèque, mais personne n’a encore voulu la couper.

Because French often uses the passé composé to talk about a completed action in the past.

Nous avons acheté = we bought / we have bought

It is built with:

• avoir in the present tense → avons
• plus the past participle → acheté

So:

• nous avons acheté = we bought

This is one of the most common ways to express the past in spoken and everyday written French.

In this sentence, acheté does not agree with pastèque.

That is because with avoir, the past participle usually stays unchanged unless the direct object comes before the verb.

Here the object comes after:

• Nous avons acheté une petite pastèque

So the participle stays:

• acheté

If the object came before, agreement could happen:

• La pastèque que nous avons achetée
  Here achetée agrees with la pastèque, which is feminine singular.

In French, some adjectives usually come before the noun, and petit/petite is one of them.

So:

• une petite pastèque = a small watermelon

Many common, short, everyday adjectives go before the noun, especially ones related to size, beauty, age, and goodness. A common memory aid is BAGS:

• Beauty
• Age
• Goodness
• Size

Since petite describes size, it normally comes before the noun.

Because pastèque is a feminine noun in French.

That affects the words connected to it:

• une = feminine singular article
• petite = feminine singular form of petit
• la = feminine singular direct object pronoun

So all of them match pastèque.

This is grammatical gender, which does not always match biological sex or any logical rule. It is simply part of the noun and must be learned with it.

Because personne means no one / nobody, and it is grammatically singular.

So French uses:

• personne n’a = no one has

Not:

• personne n’ont

Even though nobody refers to multiple possible people in meaning, it behaves as a singular subject in grammar.

This is called elision.

When ne comes before a word starting with a vowel sound, the e drops:

• ne a → n’a

The same thing happens in many common combinations:

• je ai → j’ai
• ne est → n’est
• ne ont → n’ont

So personne n’a is just the normal contracted form of personne ne a, which French does not say.

Here encore means yet.

So:

• personne n’a encore voulu = no one has wanted yet / no one has yet been willing

In affirmative sentences, encore often means still or again:

• Il dort encore = He is still sleeping
• Encore ! = Again!

But with a negative idea like this, it often corresponds to yet in English.

In compound tenses like the passé composé, adverbs often go between the auxiliary and the past participle.

So:

• n’a encore voulu

That placement is very natural in French.

Structure:

• subject → personne
• negative marker → n’
• auxiliary → a
• adverb → encore
• past participle → voulu
• infinitive → couper

Voulu is the past participle of vouloir.

Literally, vouloir means to want, so a voulu means wanted. But in this sentence, the meaning is closer to:

• has wanted to
• has been willing to
• has felt like

So:

• personne n’a encore voulu la couper

can suggest not only that nobody had the desire, but also that nobody was willing or ready to do it.

That is a very natural use of vouloir in French.

Because la is a direct object pronoun, and in French object pronouns usually come before the infinitive they belong to.

Here la refers to la pastèque.

So:

• voulu la couper = wanted to cut it

Not:

• voulu couper la

French object pronouns usually go before the verb or infinitive:

• Je vais le faire = I am going to do it
• Elle veut nous aider = She wants to help us

You do see pronouns after the verb mainly in affirmative commands:

• Coupe-la ! = Cut it!

But that is not the structure here.

Yes. La refers back to une petite pastèque.

Since pastèque is feminine singular, the pronoun is:

• la = it

So:

• la couper = to cut it

French often avoids repeating the noun and uses a pronoun instead, just as English does.

Because this is a two-verb structure:

• vouloir = to want
• couper = to cut

French keeps the first verb conjugated and leaves the second one in the infinitive:

• a voulu couper = wanted to cut

So the structure is:

• personne = no one
• n’a voulu = has wanted
• la couper = to cut it

This is very common in French:

• Je veux partir = I want to leave
• Ils ont voulu essayer = They wanted to try

Yes. That is actually a very natural English rendering.

French:

• mais personne n’a encore voulu la couper

Natural English:

• but no one has wanted to cut it yet
• but no one has been willing to cut it yet

The exact English choice depends on the tone and context, but the French grammar stays the same.