I want to say something like "After I have gone to university, I will go..."
Do I use the perfect past then future or another tense?
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Whereas in English we use the present perfect, in French you use the future perfect (futur antérieur). This is then matched with either of the normal future tenses.
(Updated) Here's that concordance in action in a sentence similar to yours:
Quand j'aurai terminé mes études, je partirai en France.
Outside of "textbook speak", it may be possible to exchange the futur antérieur for another tense (perhaps the futur simple ?). I leave it to a native speaker to weigh in or submit their own answer.
I think you could use après que instead of quand ("after" vs. "when"), but Feelew suggests otherwise. If quand sounds more natural, it might be because après que is usually paired with a subjunctive, which isn't possible in a future tense. The meaning would be the same for either choice in the future perfect, so choose what sounds most natural.
Either way, it can be changed for après alone if the subject is the same in both halves of the sentence. If you do this, then the first tense is the perfect infinitive:
Quand la pluie aura cessé, je... (Subject changes)
Après avoir terminé mes études, je... (Subject is the same)
It's also possible to use the futur simple for this first tense, but the meaning is slightly different, because it doesn't necessarily mean the action is finished.
Quand la pluie cessera, je sortirai. (The choice of verb implies that the action is over anyway)
Quand j'étudierai le français... (Alert! The future action would not be over yet)
Also, for some verbs you could combine a future with the infinitive for the second half of this structure. Compare these two versions:
Après avoir terminé mes études, je vais travailler / je travaillerai.
Après avoir terminé mes études, j'irai travailler.
To me this seems to be mainly a difference in wording: "I will work" vs. "I will go to work."