How French works
A semi-auxiliary is a verb used with an infinitive and which most commonly expresses a distinction of time (past, future etc.) or mood (possibility, wishing etc.).
These include the verb aller and the expression être sur le point de to express the near future:
Il va lui en parler demain
He is going to speak to him / her about it tomorrow
Elle est sur le point de partir
She is about to leave
And the expression venir de to express the recent past:
Ils viennent de partir en vacances
They have just gone on holiday
Semi-auxiliaries of mood are more commonly known as modals. These include:
The verb pouvoir to express possibility:
Il se peut qu'il y ait beaucoup de monde à la soirée
There may be a lot of people at the party
Fais attention! Cela pourrait exploser
Be careful! It could / might explode
J'aurais pu être tué!
I might have been killed!
Il aurait pu m'aider!
He could have helped me!
The verb devoir to express probability:
Il doit avoir dix ans maintenant
He must be ten years old now
Nous devrions arriver vers minuit
We should be there by midnight
Je ne trouve pas mes clés. J'ai dû les laisser dans la cuisine
I can't find my keys. I must have left them in the kitchen
The verbs vouloir, souhaiter, désirer to express a wish:
Je voudrais /souhaite / désire le voir
I would like to see him
The verbs devoir and falloir to express obligation:
Il doit se présenter à quatorze heures
He should turn up at 2.00 pm
Tu devrais lui écrire pour t'excuser
You ought to write to him / her and apologize
Il faut arriver une demi-heure en avance
You should arrive half an hour early
Note also the expression être censé faire which means to be supposed to do:
Elle est censée être au travail
She's supposed to be at work
The verbs pouvoir and savoir to express capability:
Vous pourrez le voir dans une demi-heure
You can see him in half an hour
Savez-vous nager?
Can you swim?
Note that savoir means to know facts:
Je sais qu'il est malade
I know he's ill
This contrasts with connaître which means to know or be acquainted with people, places:
Je connais bien Pierre / Manchester
I know Pierre / Manchester well