English modals may be followed by "have" plus a past participle to express perfect (completed) actions. Translating this construction usually requires a French verb in a perfect tense/mood followed by an infinitive.
could have = pouvoir (in
the conditional perfect)
I could have helped you.
J'aurais pu vous aider.
We could have eaten.
Nous aurions pu manger.
may/might have = peut-être, se pouvoir (plus past subjunctive)
I may/might have done it.
Je l'ai peut-être fait, Il se peut que je l'aie fait.
must have = devoir (in
the passé composé)
You must have seen it.
Vous avez dû le voir.
He must have eaten.
Il a dû manger.
shall/will have = French future perfect
I shall/will have eaten.
J'aurai mangé.
He will have arrived by noon.
Il sera arrivé avant midi.
should have = devoir (in the conditional perfect)
You should have helped.
Vous auriez dû aider.
We should have eaten.
Nous aurions dû manger.
would have = French conditional perfect
I would have helped you.
Je vous aurais aidé.
He would have eaten it.
Il l'aurait mangé.

