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.