La preuve d’achat est dans le colis.

Because de becomes d’ before a vowel sound. Since achat begins with a-, French contracts de achat to d’achat.

So:

• de + achat → d’achat

This is very common in French:

• de eau → d’eau
• de accord → d’accord

Preuve d’achat literally means proof of purchase.

It refers to something that shows you bought the item, such as:

• a receipt
• an invoice
• a purchase confirmation

In everyday situations, French may also use more specific words like ticket de caisse for a store receipt, but preuve d’achat is a broader expression.

In the expression preuve d’achat, achat is being used in a general sense: proof of purchase, not proof of the purchase or proof of a purchase.

French often leaves out the article after de in this kind of fixed expression, especially when one noun describes the type or function of another noun.

Compare:

• une salle de bain = a bathroom
• un ticket de métro = a metro ticket
• une preuve d’achat = proof of purchase

So achat here is part of the set phrase, not a separately determined noun.

French usually needs an article where English often does not.

So where English can say:

• Proof of purchase is in the package

French normally says:

• La preuve d’achat est dans le colis

That la does not necessarily mean the in a very strong or specific sense. Often it is just the normal way French introduces a noun.

Est is the verb to be, from être.

So:

• La preuve d’achat = the proof of purchase
• est = is
• dans le colis = in the package/parc el

French commonly uses être + location to say where something is:

• Le livre est sur la table. = The book is on the table.
• Les clés sont dans la voiture. = The keys are in the car.

Both can relate to a package, but they are not always identical.

• colis usually means a parcel, especially something shipped or delivered
• paquet often means a package, packet, pack, or wrapped bundle

In this sentence, colis makes good sense because it suggests a shipped parcel containing the item and the proof of purchase.

Le colis means the package, referring to a specific package already known from context.

If you said un colis, it would mean a package, which sounds less specific.

So:

• dans le colis = in the package
• dans un colis = in a package

French chooses le here because the speaker probably means the particular package being discussed.

Yes. That is also correct.

• La preuve d’achat est dans le colis = The proof of purchase is in the package.
• La preuve d’achat se trouve dans le colis = The proof of purchase is located/is found in the package.

The version with est is simpler and very natural.
The version with se trouve can sound a bit more formal or precise.

Yes, dans is the natural choice here because it means inside.

• dans le colis = inside the package

French uses dans for physical containment:

• dans la boîte = in the box
• dans le sac = in the bag

Using en here would not sound natural for this meaning.

A careful approximate pronunciation is:

la prœv da-sha eh dahn luh ko-lee

A few helpful notes:

• preuve has a vowel sound that does not exist exactly in English
• d’achat sounds like da-sha
• est is pronounced like eh
• dans has a nasal vowel; the n is not fully pronounced like English n
• colis sounds like ko-lee

Also, in normal speech, est dans may flow together smoothly.