Le client paie lorsque la facture de régularisation arrive.

In French, you usually need an article before a singular countable noun. So client normally appears as le client, un client, ce client, etc.

Here, le client can mean:

• the client in a specific context, or
• the client/customer in a general, category-like sense

French often uses the definite article this way where English might be more flexible.

Payer is the infinitive, meaning to pay.
In the sentence, the verb is conjugated to match le client:

• je paie
• tu paies
• il/elle paie
• nous payons
• vous payez
• ils/elles paient

So le client paie means the client pays.

A small spelling note: with payer, you may also see forms like paye. Both spellings exist in modern French, but paie is very common.

Yes, quand would also be possible in many contexts.

• lorsque = when
• quand = when

The difference is mostly one of style:

• lorsque is often a bit more formal or written
• quand is more common in everyday speech

So this sentence sounds slightly more formal with lorsque, but not unnatural.

Grammatically, this is a noun phrase:

• facture = invoice/bill
• de régularisation = for adjustment/regularization

So facture de régularisation means a bill or invoice that adjusts a previous amount. In practical terms, it is often a final adjustment invoice, balancing bill, or true-up bill.

This kind of structure is very common in French:

• un ticket de caisse
• une salle de bain
• une facture d’électricité

It is basically noun + de + noun.

Because de régularisation is functioning like a type or category, not like of the regularization.

French often leaves out the article after de in expressions where the second noun describes the first:

• une tasse de thé
• une table de cuisine
• une note de service
• une facture de régularisation

If you added an article, the meaning would usually change or sound much less natural.

Because French often uses the present tense for general truths, repeated situations, or standard procedures.

So this sentence sounds like:

• whenever that invoice arrives, the client pays
• that is the normal sequence of events

Both verbs are in the present because the sentence describes a general rule or habitual situation:

• Le client paie
• lorsque la facture ... arrive

If you were talking about one specific future event, French might use future forms instead:

• Le client paiera lorsque la facture de régularisation arrivera.

But for a general statement, the present is very natural.

Yes. In French, arriver is often used quite broadly for documents, letters, bills, emails, and so on.

So la facture ... arrive can mean:

• the invoice arrives
• the invoice comes in
• the invoice is received

It does not have to mean literal physical movement in a dramatic sense. It is a normal verb to use for paperwork.

Client is the masculine form. The feminine form is cliente.

So you could say:

• Le client paie... for a male customer or a generic customer in some contexts
• La cliente paie... for a female customer

In business French, client is often used generically, but if you know the person is female, cliente is perfectly normal.

The word order is very standard French:

• Le client paie = subject + verb
• lorsque la facture de régularisation arrive = conjunction + subject + verb

French does not need a word like does here, and it does not change the order the way English sometimes does in questions.

So this is a straightforward statement: subject + verb + subordinate clause.

Paie is pronounced roughly like peh or pay, depending on accent and speaker, but the safest learner approximation is something like peh.

A few pronunciation notes:

• paie and paient are often pronounced the same
• the final -e is not pronounced
• ai here usually gives an open vowel sound, not a fully English pay sound

So an English speaker should avoid overpronouncing it like a strong English pay. A softer French vowel is better.

Before a vowel sound, lorsque usually drops the final e and becomes lorsqu’:

• lorsqu’il arrive
• lorsqu’elle paie

That is just like many other French words that elide before a vowel.

In your sentence, the next word is la, which starts with a consonant sound, so it stays lorsque.