Le secouriste voit à quel point Paul s’étouffe vite.

In French, singular countable nouns usually need an article.

So le secouriste means the first-aider / the rescuer / the emergency responder.

You would not normally say just secouriste by itself in a sentence like this, just as in English you would not usually say Rescuer sees... You would say The rescuer sees...

À quel point means something like:

• how much
• to what extent
• how
• just how

So voit à quel point Paul s’étouffe vite means the rescuer sees how quickly / to what extent Paul is choking.

It is a very common expression in French for emphasizing degree or intensity.

Examples:

• Tu ne sais pas à quel point je suis fatigué. = You don’t know how tired I am.
• Elle comprend à quel point c’est grave. = She understands how serious it is.

Because s’étouffer is a reflexive verb, and in this context it means to choke or to suffocate.

The basic verb étouffer can mean:

• to smother
• to stifle
• to suffocate someone/something

But s’étouffer means that the subject is undergoing the choking himself:

• Paul s’étouffe = Paul is choking

So the se part is important here.

Compare:

• Il étouffe le feu. = He smothers the fire.
• Il s’étouffe. = He is choking.

This is just elision.

Se becomes s’ before a vowel sound, to make pronunciation smoother.

So:

• se + étouffe → s’étouffe

The same happens with many other little words:

• je aime → j’aime
• le ami → l’ami
• ne écoute pas → n’écoute pas

Both are in the present tense.

• voit = from voir = sees
• s’étouffe = from s’étouffer = is choking / chokes

French often uses the simple present where English might use either:

• a simple present: sees
• or a progressive form: is seeing, is choking

So depending on context, Paul s’étouffe can be understood as:

• Paul is choking
• or less naturally in English, Paul chokes

Here, is choking is the natural translation.

Vite is an adverb meaning quickly / fast.

In French, adverbs often come after the verb they modify, especially in simple structures.

So:

• Paul s’étouffe vite = Paul chokes quickly / is choking quickly

That word order is normal in French.

English is similar here:

• Paul is choking quickly
• Paul quickly chokes

French most naturally uses:

• verb + adverb
  so s’étouffe vite

It can correspond to either one in English, depending on the sentence.

Here it functions as an adverb, so quickly is the better match:

• Paul s’étouffe vite = Paul is choking quickly

In everyday French, vite is extremely common and often covers both ideas that English separates into fast and quickly.

Examples:

• Il court vite. = He runs fast.
• Dépêche-toi vite ! = Hurry up quickly!

Because this sentence is not structured as He sees that Paul is choking quickly.

Instead, it is structured as:

• He sees how quickly Paul is choking
• He sees to what extent Paul is choking quickly

So after voit, French uses à quel point, which introduces an indirect exclamation or degree clause, not a simple that-clause.

Compare:

• Le secouriste voit que Paul s’étouffe. = The rescuer sees that Paul is choking.
• Le secouriste voit à quel point Paul s’étouffe vite. = The rescuer sees how quickly / to what extent Paul is choking.

The second version emphasizes degree.

Sometimes yes, but à quel point is especially natural when talking about degree or intensity.

For example:

• Il voit à quel point c’est grave.
• Il voit combien c’est grave.

Both can work, but à quel point often sounds especially clear when you mean to what extent.

In this sentence, à quel point is a very natural choice.

Not always.

It can mean:

• literal choking
• suffocating
• sometimes figuratively being overwhelmed or unable to breathe properly

But in a sentence with Le secouriste and Paul s’étouffe, the most natural reading is literal physical choking, because the context suggests a medical emergency.

Because the subject is already stated explicitly: Le secouriste.

French needs a subject, but that subject can be:

• a noun phrase: Le secouriste voit...
• or a pronoun: Il voit...

You do not use both unless you are doing dislocation for emphasis, which is a different structure:

• Le secouriste, il voit à quel point Paul s’étouffe vite.

That version is possible in spoken French, but the normal written sentence is simply:

• Le secouriste voit à quel point Paul s’étouffe vite.

Most directly, vite modifies s’étouffe.

So the literal structure is:

• Paul s’étouffe vite = Paul is choking quickly / Paul chokes quickly

Then à quel point comments on the degree:

• voit à quel point... = sees how much / sees how...

So the overall meaning is that the rescuer perceives how quickly Paul is choking.

In natural English, you might translate the whole thing more idiomatically rather than word-for-word, but grammatically vite belongs with s’étouffe.