Elle était en train de se coiffer quand la professeure a envoyé un message sur le questionnaire de demain.

Était is the imparfait, which is often used for an action or situation that was in progress in the past.

Here, Elle était en train de se coiffer means she was in the middle of brushing/combing/do­ing her hair.

• est would be present tense: she is doing it now
• a été would mean has been / was in a completed sense, which does not fit this ongoing background action

So était is used because this action was ongoing when something else happened.

En train de + infinitive means in the middle of doing something or currently doing something.

So:

• être en train de se coiffer = to be in the process of doing one’s hair

It is a common way in French to stress that an action is happening right then, similar to the English be + -ing form.

Compare:

• Elle se coiffait = she was doing her hair
• Elle était en train de se coiffer = she was right in the middle of doing her hair

The second version is a bit more explicit.

Se coiffer is a reflexive verb. The se shows that the person is doing the action to themselves.

So:

• coiffer quelqu’un = to do/style/brush someone’s hair
• se coiffer = to do/style/brush one’s own hair

In this sentence, elle is the one doing her own hair, so French uses the reflexive form.

After en train de, French uses the infinitive.

So the structure is:

• être en train de + infinitive

Examples:

• Elle est en train de lire = She is reading
• Nous sommes en train de manger = We are eating
• Elle était en train de se coiffer = She was doing her hair

Because se coiffer is reflexive, the reflexive pronoun stays attached to the infinitive: se coiffer.

A envoyé is the passé composé, which is often used for a completed event in the past.

In this sentence:

• Elle était en train de se coiffer = background action in progress
• la professeure a envoyé un message = the interrupting event that happened

This is a very common French pattern:

• imparfait for what was going on
• passé composé for what happened during that time

So the teacher’s sending the message is treated as a single completed event.

Quand means when and connects the two parts of the sentence.

It introduces the moment when the second action happened:

• Elle était en train de se coiffer quand...
• She was doing her hair when...

In sentences like this, quand often introduces the event in the passé composé that occurred during an ongoing action in the imparfait.

La professeure is a feminine form meaning the female teacher/professor.

French job titles can often change form depending on gender:

• le professeur = a male teacher/professor
• la professeure = a female teacher/professor

Usage can vary by region and style, and you may also see la professeur in some contexts, but la professeure is now very common and standard in many places.

Here, sur means about or regarding.

So:

• un message sur le questionnaire de demain = a message about tomorrow’s quiz/questionnaire

French often uses sur where English would use about.

Examples:

• un livre sur l’histoire = a book about history
• une discussion sur le problème = a discussion about the problem

So sur does not mean physical on here.

De demain means of tomorrow or more naturally in English, tomorrow’s.

So:

• le questionnaire de demain = tomorrow’s quiz / the quiz for tomorrow

French often uses de + time expression where English uses a possessive or adjective-like structure.

Examples:

• le cours de demain = tomorrow’s class
• la réunion de ce soir = tonight’s meeting
• le match de dimanche = Sunday’s game

You do not say du demain here because demain is being used as a time word, and de demain is the normal expression.

Yes. Se coiffer can mean several related things depending on context:

• to brush one’s hair
• to comb one’s hair
• to do one’s hair
• to style one’s hair

It does not always refer to one exact action. It can mean the general process of fixing or arranging your hair.

So the best English translation depends on the situation.

In a envoyé, the verb is formed with avoir:

• a = has
• envoyé = sent

With avoir, the past participle usually does not agree with the subject.

So even though la professeure is feminine singular, we still write:

• la professeure a envoyé

not a feminine-marked form.

Agreement with a past participle is a bigger topic in French, but in this sentence there is no change needed.

Yes. Elle se coiffait quand la professeure a envoyé un message... is also correct.

The difference is mainly one of emphasis:

• Elle se coiffait = she was doing her hair
• Elle était en train de se coiffer = she was in the middle of doing her hair

Using en train de makes the ongoing action more explicit and vivid. It highlights that the action was actively happening at that moment.