In the French language, semi-auxiliaries are the same as in the English language.  They are multi-word verbs that occur before main verbs.  In English, these semi-auxiliaries include: have to, get to, be about to, used to, mean to, be going to, etc.

In French, many of the semi-auxiliaries are the same as the English ones.

To express the future:
ALLER + infinitive (near future)
Mon bébé va s’endormir.  (My baby is going to go to sleep).
J’allais partir quand mon copain est arrivé.  (I was going to leave when my boyfriend arrived.)

***Be careful though as aller + infinitive can be used to express movement and in that case, it is not considered a semi-auxiliary.  Ex: El bébé va marcher.

ÊTRE SUR LE POINT DE + infinitive (immediate future)
Nous sommes à table ; nous sommes sur le point de manger.  (We are at the table.  We are about to eat.)

DEVOIR + infinitive
Mes amis doivent arriver à la gare ce soir à 8 heures. (My friends should be arriving at the station this evening at 8 o’clock.)

To express the past:
VENIR DE + infinitive (recent past)
Mon mari n’est pas là ; il vient de sortir. (My husband is not here; he just left.)

To express duration:
ÊTRE EN TRAIN DE + infinitive
J’étais en train de faire le linge quand le lave-linge s’est brisé. (I was doing the laundry when the washer broke down.)

To express the beginning of an action:
COMMENCER À / SE METTRE À + infinitive
Les gens commencent à arriver.  (The people are starting to arrive.)
Tout le monde s’est mis à rire.  (Everybody started to laugh.)

To express the end of an action:
FINIR DE / CESSER DE / S’ARRÊTER DE + infinitive
J’ai fini d‘écrire le livre.  (I’ve finished writing the book.)
La neige a cessé de tomber.  (The snow has stopped falling.)
Je lui ai demandé de s’arrêter de fumer ; donc, il a éteint sa cigarette.  (I asked him to stop smoking so he put out his cigarette.)

**Be careful, cesser de and arrêter de in the negative form express duration.
Ex: La neige ne cesse de tomber.  (The snow keeps falling.)
Il n’arrête pas de fumer.  (He smokes all the time.)

To express probability:
DEVOIR + infinitive
J’ai faim; il doit être environ midi. (I’m hungry.  It must be around noon.)
POUVOIR + infinitive
La salle est pleine; il peut y avoir 500 personnes. (The hall is full; there could be 500 people here.)

To express obligation:
DEVOIR + infinitive
On doit éteindre les portables. (Cell phones must be turned off.)

But, be careful, some of these multi-word verbs may occur in other contexts in which they are not considered to be semi-auxiliaries.  You will know this when there is no other main verb.  For example:

DEVOIR: Je dois beaucoup à mes parents. (I owe a lot to my parents.)