Au fur et à mesure que son exposé approche, Marie se sent de plus en plus prête.

It means as, as time goes on, or gradually as.

It introduces the idea that one thing changes little by little while something else is happening.

In this sentence:

Au fur et à mesure que son exposé approche...
= As her presentation gets closer...

It is a fixed expression, so it is best learned as a whole.

Because que introduces a whole clause with a verb.

Here, the clause is:

son exposé approche

So:

• au fur et à mesure que + clause
• au fur et à mesure de + noun

Compare:

• Au fur et à mesure que le temps passe = As time goes by
• Au fur et à mesure de la journée = As the day goes on / over the course of the day

Because exposé is a masculine noun in French.

Possessive adjectives agree with the noun possessed, not with the owner.

So:

• son exposé = her presentation
• sa voiture = her car

Even though Marie is female, the noun exposé is masculine, so French uses son.

Here, un exposé means a presentation, a talk, or an oral report.

It often refers to something a student or speaker presents in front of others.

So son exposé means her presentation.

Yes. In French, just like in English, an event can be described as approaching or getting closer.

So:

• son exposé approche = her presentation is approaching
• more natural English: her presentation is getting closer

The subject is son exposé, so the verb is in the third person singular:

• approcher → approche

Because the verb here is se sentir, which means to feel in the sense of being in a certain state.

So:

• Marie se sent prête = Marie feels ready

This structure is very common:

• se sentir bien = to feel well
• se sentir fatigué = to feel tired
• se sentir prêt = to feel ready

Without the reflexive pronoun, sentir often means to smell or to feel/sense something:

• Je sens une odeur = I smell an odor
• Je sens le vent = I feel the wind

So se sentir is the form you want when talking about how someone feels internally.

It means more and more.

It is used to show gradual increase.

Pattern:

• de plus en plus + adjective
• de plus en plus + adverb

Examples:

• de plus en plus important = more and more important
• de plus en plus vite = faster and faster / more and more quickly

Here:

• de plus en plus prête = more and more ready

The opposite is de moins en moins = less and less.

Because prête agrees with Marie, who is feminine.

The adjective is prêt / prête:

• masculine: prêt
• feminine: prête

Since Marie se sent prête, the adjective describes Marie, so it must match her gender.

Compare:

• Paul se sent prêt
• Marie se sent prête

Because French often uses the present tense for something that is happening now or developing gradually.

This sentence describes an ongoing process:

• the presentation is getting closer
• Marie feels increasingly ready

So the present tense is natural:

• approche
• se sent

In English, we also often use the present in this kind of structure:

• As her presentation approaches, Marie feels more and more ready.

Yes. À mesure que is very common and usually means the same thing.

So you could also say:

À mesure que son exposé approche, Marie se sent de plus en plus prête.

Both are correct.
Au fur et à mesure que can feel a little more emphatic or a little more explicitly gradual, but in many contexts they are interchangeable.

Usually, yes, but it depends on context.

In this sentence, prête means ready/prepared in a mental or practical sense.

So:

• Marie se sent prête = Marie feels ready

It suggests she feels prepared for the presentation.

If you wanted to stress that she has prepared her talk, French might also use verbs like préparer in other contexts, but se sentir prête is exactly right for describing her state of mind.

Yes. A common alternative is a plus... plus... structure:

Plus son exposé approche, plus Marie se sent prête.

This means: The closer her presentation gets, the more ready Marie feels.

So the original sentence and this version are both natural; they just package the idea a little differently.