Pour boucher le petit trou près du toit, Paul achète un produit utile.

Pour + infinitive is a very common French way to express purpose: in order to / to do something.

So:

• pour boucher = to plug up / in order to seal
• Pour boucher le petit trou... = To plug the small hole...

This is similar to English to or in order to:

• Je viens pour aider. = I’m coming to help.
• Elle part pour travailler. = She’s leaving to work.

Here, boucher means to block, plug, stop up, or seal an opening.

In this sentence, it fits a hole:

• boucher un trou = to plug a hole

Be careful not to confuse it with:

• la bouche = mouth
• le boucher = the butcher

They are related in form, but in this sentence boucher is clearly the verb to plug/seal up.

Le means the, so le petit trou refers to a specific hole, not just any hole.

• un petit trou = a small hole (not specific)
• le petit trou = the small hole (already identified or known in context)

Even if English might sometimes say a small hole, French often uses the definite article when the thing is understood from the situation.

In French, most adjectives come after the noun, but some common short adjectives often come before it. Petit is one of them.

So:

• un petit trou = a small hole

This is part of a common group often remembered as BAGS adjectives:

• Beauty
• Age
• Goodness
• Size

Since petit expresses size, it usually goes before the noun.

Because près is normally followed by de.

So the structure is:

• près de = near

Then:

• de + le = du

That gives:

• près du toit = near the roof

Similar examples:

• près de la maison = near the house
• près des arbres = near the trees

So près le toit is not correct here.

Du is a contraction of de + le.

Since toit is masculine singular:

• le toit = the roof

After près de, you get:

• près de le toit → près du toit

This kind of contraction is very common in French:

• de + le = du
• de + les = des
• à + le = au
• à + les = aux

The accent shows the verb form and pronunciation.

The verb is acheter = to buy.
In the je / tu / il / elle / on forms of the present tense, the e in the stem often changes to è:

• j’achète
• tu achètes
• il/elle/on achète

But:

• nous achetons
• vous achetez
• ils/elles achètent

So Paul achète means Paul buys / is buying.

The è helps show the open vowel sound.

Because after the subject Paul, you need a conjugated verb, not the infinitive.

• acheter = to buy (infinitive)
• achète = buys / is buying (present tense, il/elle/on form)

Since Paul is third-person singular, the correct form is:

• Paul achète

Just like:

• I buy → j’achète
• Paul buys → Paul achète

Most French adjectives come after the noun, and utile is one of them.

So:

• un produit utile = a useful product

This is the normal order:

• noun + adjective

Examples:

• un livre intéressant = an interesting book
• une idée utile = a useful idea

Unlike petit, which often goes before the noun, utile usually stays after it.

Yes. Produit often does mean product, but in context it can also mean a substance, item, treatment, compound, or material.

In this sentence, it probably means something like:

• a useful product
• a useful material
• a useful sealant/filler item

French often uses produit in a broad way, especially for something practical or commercial.

Yes, the main verb achète is in the present tense.

• Paul achète literally = Paul buys

But in English, depending on context, you might translate it as:

• Paul buys
• Paul is buying
• Paul buys a useful product to plug the small hole near the roof

French present tense often covers both the simple present and the present progressive meanings that English separates.

It breaks down like this:

• Pour boucher le petit trou près du toit = purpose phrase
  (To plug the small hole near the roof)

• Paul = subject

• achète = verb

• un produit utile = direct object
  (a useful product)

So the full structure is:

purpose phrase + subject + verb + object

That makes the sentence feel like:

To seal the small hole near the roof, Paul buys a useful product.