Le secouriste alerte le professeur après l’appel d’urgence.

They are doing two different jobs:

• Le secouriste = the first aider / the rescuer
  Here, le is the definite article before the subject noun.

• le professeur = the teacher
  Here, le is the definite article before the direct object noun.

So French, like English, can use the more than once in the same sentence:

• The rescuer alerts the teacher ...

Both secouriste and professeur are introduced with le because they are masculine singular nouns in this sentence.

Because French usually shortens le or la before a vowel sound.

• le + appel becomes l’appel

This is called elision. It happens to avoid a clash of vowel sounds.

Other examples:

• l’école instead of la école
• l’ami instead of le ami

So l’appel d’urgence means the emergency call, and l’ stands in for le here.

In this sentence, alerte is a verb, from alerter, meaning to alert, to warn, or to notify.

So:

• Le secouriste alerte le professeur = The first aider alerts the teacher

This is not the noun une alerte meaning an alert.

Here it is the third-person singular present tense form:

• j’alerte = I alert
• tu alertes = you alert
• il/elle alerte = he/she alerts

Because le professeur is the direct object of the verb alerter.

In English, we often say:

• alert someone

French works the same way here:

• alerter quelqu’un

So:

• Le secouriste alerte le professeur not
• Le secouriste alerte au professeur

Some French verbs do require a preposition, but alerter normally takes a direct object.

Après means after.

In this sentence:

• après l’appel d’urgence = after the emergency call

It introduces a time expression telling us when the rescuer alerts the teacher.

French word order here is very similar to English:

• Le secouriste = subject
• alerte = verb
• le professeur = object
• après l’appel d’urgence = time phrase

So the structure is: Subject + verb + object + time expression

For the same reason as l’appel: French shortens de before a vowel.

• de + urgence becomes d’urgence

This is another example of elision.

So:

• appel d’urgence = emergency call

Literally, this is something like call of emergency, but in natural English we say emergency call.

Yes, it is a very common expression.

• un appel d’urgence = an emergency call
• l’appel d’urgence = the emergency call

French often uses noun + de + noun where English may use an adjective or a compound noun.

Examples:

• une salle de classe = classroom
• une carte d’identité = identity card
• un numéro de téléphone = telephone number

So appel d’urgence is a normal and natural French way to say emergency call.

Secouriste can refer to either a man or a woman. The form of the noun often stays the same; the article changes.

• le secouriste = the male first aider / rescuer
• la secouriste = the female first aider / rescuer

So in your sentence, le secouriste tells you the person is masculine.

The same idea often applies to professeur:

• le professeur
• la professeure or sometimes la professeur, depending on style and region

Because French professeur has a broader meaning than English professor.

In French, professeur can mean:

• a school teacher
• a secondary-school teacher
• sometimes a university professor, depending on context

So in many learning sentences, le professeur is best translated as the teacher unless the context clearly points to a university professor.

A few useful pronunciation notes:

• Le secouriste
  The final -e in le is very light.
  In secouriste, the final -te is pronounced.

• alerte
  Sounds roughly like a-lert with a pronounced final t sound.

• après
  The è is an open vowel, like eh.

• l’appel
  The ll does not sound like English ll in call.
  It sounds roughly like ah-pel.

• d’urgence
  urgence begins with a vowel sound, so d’urgence links smoothly.
  The French r is different from the English r.

Also, in natural speech, French flows together:

• Le secouriste alerte le professeur après l’appel d’urgence

Practising it in chunks helps:

• Le secouriste
• alerte le professeur
• après l’appel d’urgence

Yes, alerte is in the present tense.

Grammatically, it means:

• The rescuer alerts the teacher

But depending on context, French present tense can sometimes be used in a more vivid narrative style, where English might use the present or the past.

If you wanted a clear past tense, you would usually say:

• Le secouriste a alerté le professeur après l’appel d’urgence. = The rescuer alerted the teacher after the emergency call.

So your sentence is straightforwardly present tense, but context always matters.

Yes, French can move time expressions around, although the version you have is very natural.

You could also say:

• Après l’appel d’urgence, le secouriste alerte le professeur.

This puts more emphasis on the timing: After the emergency call...

Both are correct. The original version is neutral and simple:

• Le secouriste alerte le professeur après l’appel d’urgence.