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For the Coffee Break French (a podcast that teaches French) season 3 episode 11, at the 10:15 mark, I think I hear the following:

Cette semaine, en cours, nous avons du parler de notre routine quotidienne.

I may have gotten some of the words incorrect, but I definitely hear "nous avons du parler".

I have never seen this construction before. I have seen de + infinitive before, but never du + infinitive. Can someone explain what construction is being used here, so I can Google it and learn about it?

2

This is not du. Dû is the past participle of the verb "devoir", so the tense of "nous avons dû" is passé composé.

We had to talk about our daily routine.

3

Note that while not used in the sentence you heard, du + infinitive is somewhat possible in French, when the infinitive is actually (used as) a noun representing something uncountable. For example:

  • Les narines devaient être dans la même situation, parce que l’odeur monte aussi ; et il les fallait près de la bouche, parce qu’elles nous aident beaucoup à juger du boire et du manger.
    Génie du christianisme - Chateaubriand
  • Les premières leçons de la vue, du goût, du toucher, du marcher et du parler.
    Harmonies de l'enfance - Bernardin de Saint Pierre
  • This is interesting! I never knew an infinitive could sometimes be used as a noun! – silph Jul 21 '16 at 14:54
  • 2
    Well, technically, the infinitive is the nominal form (or mode) of a verb. etudes-litteraires.com/infinitif.php – jlliagre Jul 21 '16 at 14:57
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To complete Stéphane's answer (I can not comment yet), you can use it to mean 'had to':

J'ai dû + inf
Tu as dû + inf
Il a dû + inf
Nous avons dû + inf
Vous avez dû + inf
Ils / elles ont dû + inf

"J'ai dû prendre le bus" for example :)

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