Le procès-verbal indique que la majorité a approuvé la résolution.

In this context, un procès-verbal means the official minutes or official record of a meeting.

A word-for-word breakdown would not help much, because this is a fixed expression in French. In everyday modern usage, you should learn procès-verbal as a single unit of meaning.

A few notes:

• In meeting contexts, procès-verbal = minutes / record of proceedings
• In legal or police contexts, it can also mean official report

So in this sentence, it most naturally refers to the written record of a meeting or decision.

Le is the definite article, so it means the rather than a.

That suggests the speaker is referring to a specific, known document:

• Le procès-verbal = the minutes / the official record
• Un procès-verbal = a set of minutes / an official record

French often uses the definite article when the thing is already identified by the situation or context.

Because procès-verbal is a fixed compound noun in French, and it is traditionally written with a hyphen.

It is best to memorize it in its full written form:

• un procès-verbal
• le procès-verbal

Its plural is:

• des procès-verbaux

That plural is worth learning because it is irregular.

Because la majorité is grammatically singular.

Even though it refers to many people, the head noun is majorité, which is singular, so the verb is singular too:

• la majorité a approuvé = the majority approved

This is similar to how English can also treat the majority as singular, especially in formal usage.

You may sometimes see variation in agreement in other contexts, especially when the sentence emphasizes the people inside the group, but here the standard grammar is singular.

A approuvé is the passé composé, one of the main past tenses in French.

It is formed with:

• the auxiliary verb avoir in the present: a
• the past participle: approuvé

So:

• a approuvé = approved / has approved

In this sentence, it refers to a completed action: the approval happened and is treated as a finished event.

Because approuver takes avoir in the passé composé, and with avoir, the past participle usually does not agree with the subject.

So:

• la majorité a approuvé
• le conseil a approuvé
• les membres ont approuvé

The participle stays approuvé unless there is a direct object placed before the verb, which is not the case here.

Que introduces a subordinate clause, meaning that.

So the structure is:

• Le procès-verbal indique = The minutes indicate
• que la majorité a approuvé la résolution = that the majority approved the resolution

In English, that is sometimes optional:

• The minutes indicate that the majority approved the resolution
• The minutes indicate the majority approved the resolution

In French, que is normally required here.

Because the sentence combines:

• a present fact: the minutes indicate
• a past event: the majority approved

This is very natural in both French and English.

The idea is:

• the document currently says / shows
• that something happened earlier

So the tense contrast is logical:

• indique = what the document says now
• a approuvé = what happened at the meeting

They are related, but not identical.

• approuver means to approve
• voter pour means to vote in favor of

If a majority a approuvé la résolution, the focus is on the result: the resolution was approved.

If you say la majorité a voté pour la résolution, the focus is on the act of voting in favor of it.

In many contexts they may be close in meaning, but approuver is slightly more general and often sounds formal.

Résolution is a feminine noun, so it takes the feminine singular article la.

So:

• la résolution = the resolution

This is simply something to memorize with the noun:

• une résolution
• la résolution

Also, in formal or institutional contexts, résolution often means an official decision or motion.

No. It depends on whether it is definite or indefinite.

Examples:

• la majorité = the majority
• une majorité = a majority

In your sentence, la majorité refers to the majority in a specific group, such as the voters or members at a meeting, so the definite article makes sense.

A natural pronunciation would be approximately:

Le procès-verbal indique que la majorité a approuvé la résolution.

A rough guide for an English speaker:

• Le ≈ luh
• procès-verbal ≈ პრო-say ver-bal
• indique ≈ an-deek
• que ≈ kuh
• la majorité ≈ la ma-zho-ree-tay
• a approuvé ≈ ah ah-proo-vay
• la résolution ≈ la ray-zo-loo-syon

A couple of useful pronunciation points:

• The s in résolution sounds like z
• majorité has the zh sound, like the s in measure
• a approuvé may sound quite smooth in fast speech, even though it is written as two words

Not usually in a formal sentence like this.

• indique means indicates / states / shows
• dit means says

A document can technically dit in some contexts, but indique is much more natural and formal when talking about official records, reports, and written documents.

So:

• Le procès-verbal indique que... sounds appropriate and formal
• Le procès-verbal dit que... sounds less natural here

Yes, definitely. The vocabulary is formal and administrative:

• procès-verbal
• majorité
• approuvé
• résolution

This is the kind of sentence you might see in:

• meeting minutes
• official reports
• legal or institutional documents
• corporate or governmental contexts

It is correct, natural French, but not especially conversational.