French, like several other Romance languages, keeps a separate mood beyond simple fact-stating — the subjunctive — for sentences shaped by a wish, a doubt, an emotion, a necessity, or an attempt to influence someone else. It's almost always triggered by a specific phrase before que earlier in the sentence, so once the common triggers become familiar, choosing the mood mostly stops being a puzzle. A few, like espérer que, are exceptions worth learning on their own.
Indicative states what's real. Subjunctive shows up the moment a sentence expresses a wish, a doubt, an emotion, or an attempt to influence someone else.
Stating what's real or certain
Triggered by wishes, doubts, emotions, and influence
Je crois qu'il a raison, mais je ne crois pas qu'il soit facile à convaincre.
I think he's right, but I don't think he's easy to convince.
Croire que triggers the indicative when it states a belief, but ne pas croire que flips to subjunctive — denying certainty is itself a kind of doubt.
Take the quiz and see if you can spot the triggers that call for the subjunctive.