Elle a refusé de partir plus tôt, et j’ai insisté pour l’attendre après le cours.

This is the passé composé, the most common past tense for completed actions in everyday French.

• elle a refusé = she refused
• j’ai insisté = I insisted

It is formed with:

• a present-tense auxiliary verb, here avoir
• a past participle, here refusé and insisté

So:

• a refusé = has refused / refused
• ai insisté = have insisted / insisted

In English, we usually translate these as simple past.

Because refuser is normally followed by de + infinitive when another verb comes after it.

The pattern is:

refuser de + verb

So:

• refuser de partir = to refuse to leave
• refuser de parler = to refuse to speak

This is just a verb pattern you need to learn. French often requires a preposition where English does not.

After insister, French often uses pour + infinitive to mean to insist on doing something or to insist that something be done.

So:

• j’ai insisté pour l’attendre = I insisted on waiting for her

Here, pour is part of the construction with insister. You should not try to translate it word-for-word as English for every time.

A useful takeaway is:

• refuser de + infinitive
• insister pour + infinitive

Different French verbs require different prepositions.

Because they follow another verb and describe a second action.

In this sentence:

• Elle a refusé de partir: she refused to leave
• J’ai insisté pour l’attendre: I insisted on waiting for her

French often uses the infinitive after a conjugated verb when the subject of both actions is the same.

Here:

• elle is the one who refused and the one who would leave
• je am the one who insisted and the one who would wait

If the subject changes, French often uses que + another verb form instead.

It stands for la, meaning her.

So:

• l’attendre = attendre + la = to wait for her

Because attendre begins with a vowel, la becomes l’.

In this sentence, l’ refers back to elle.

Because French object pronouns normally go before the verb they belong to.

So French says:

• l’attendre

not:

• attendre-la

With an infinitive, the object pronoun usually goes directly in front of that infinitive:

• Je veux le voir = I want to see him
• pour l’attendre = to wait for her

This often feels unusual to English speakers, but it is standard French word order.

Because French attendre takes a direct object.

English says:

• wait for someone

French says:

• attendre quelqu’un

So:

• attendre Marie = wait for Marie
• l’attendre = wait for her

This is a very common difference between English and French. You do not say attendre pour elle in this meaning.

Plus tôt means earlier or sooner.

In this sentence, it modifies partir:

• partir plus tôt = to leave earlier

Even though plus often means more, the expression plus tôt is the normal way to say earlier.

Compare:

• plus tôt = earlier
• plus tard = later

In this context, le cours most naturally means the class or the lesson.

So:

• après le cours = after class / after the lesson

French cours can refer to:

• a class session
• a lesson
• sometimes a course in a broader sense

In a sentence like this, English would usually say after class.

This is called elision. French often drops a vowel before another vowel or a silent h.

So:

• je ai becomes j’ai
• la attendre becomes l’attendre

This makes pronunciation smoother and is required in standard French spelling.

Then French would usually stop using the infinitive and use que + a conjugated verb instead.

For example:

• J’ai insisté pour qu’il l’attende après le cours
  = I insisted that he wait for her after class.

That is because the original sentence uses the infinitive partly because I am both:

• the one who insisted
• the one who would wait

When the subject changes, French often switches to a full clause.