Learn Hardcore French: Elle est nerveuse parce qu'elle ne croit pas qu'ils aient compris la nouvelle loi. - She is nervous because she does not believe that they have understood the new law.

Indicative when the speaker affirms belief or is fairly sure:
- Elle croit qu'ils ont compris. – She believes they understood.
Subjunctive when the belief is denied, doubted, or questioned:
- Elle ne croit pas qu'ils aient compris. – She doesn’t believe they (really) understood.

In everyday spoken French, many people still say qu'ils ont compris even in the negative, but the subjunctive is the standard, more careful form here and fits well in written or formal French.

Exactly when does croire que take the subjunctive and when the indicative?

Basic pattern:

Affirmative (speaker believes it):
→ Indicative
- Je crois qu'il a raison. – I think he’s right.
Negative or interrogative (doubt, uncertainty):
→ Often subjunctive, especially in careful French
- Je ne crois pas qu'il ait raison. – I don’t think he’s right.
- Crois-tu qu'il ait raison ? – Do you think he’s (really) right?

However:

In spoken French, you will very often hear the indicative even after ne pas croire:
- Je ne crois pas qu'il a raison. (common, but less “textbook-correct”)
If the speaker actually does believe the thing, even in a question or negative, they may choose the indicative to show certainty:
- Tu ne crois pas qu'il a raison ? (implies: I think he is right, don’t you?)

So the subjunctive is about the speaker’s attitude (doubt/uncertainty), not just about the verb croire mechanically.

What tense exactly is aient compris, and how is it formed?

aient compris is past subjunctive (subjonctif passé).

Formation:

Present subjunctive of the auxiliary avoir or être
- avoir (present subjunctive):
  - j’aie, tu aies, il/elle/on ait, nous ayons, vous ayez, ils/elles aient
- the past participle of the main verb.

For comprendre:

Auxiliary: avoir
Past participle: compris

So:

ils aient compris = they have understood (in the subjunctive mood).

Use:

It’s used when the action is completed and before or at the same time as the main clause, but the mood is subjunctive because of doubt/feeling/necessity, etc.
- Elle est nerveuse parce qu'elle ne croit pas qu'ils aient compris.
  → She’s nervous because she doesn’t believe they have understood (that prior event).

Could we say qu'ils comprennent la nouvelle loi instead of qu'ils aient compris la nouvelle loi? What’s the difference?

Yes, grammatically you can say:

Elle est nerveuse parce qu'elle ne croit pas qu'ils comprennent la nouvelle loi.

Difference:

qu'ils aient compris (past subjunctive)
→ Focus on a finished act of understanding:
that they have already understood it (by now).
qu'ils comprennent (present subjunctive)
→ Focus on their current state of understanding or ability:
that they understand it (in general / right now).

In your sentence, aient compris matches the idea that the law was explained and she doubts they understood it properly already.
comprennent would be more like doubting their ongoing grasp of the law.

Why is it nerveuse and not nerveux?

Because adjectives in French must agree in gender and number with the noun or pronoun they describe.

Subject: elle → feminine singular.
Base adjective: nerveux (masculine singular).
Feminine singular form: nerveuse.

Summary of the main forms:

masculine singular: nerveux
feminine singular: nerveuse
masculine plural: nerveux
feminine plural: nerveuses

So:

Il est nerveux. – He is nervous.
Elle est nerveuse. – She is nervous.

Why do we write qu'elle and qu'ils instead of que elle and que ils?

This is due to elision in French: que becomes qu' before a word starting with a vowel sound (or mute h).

que
- elle → qu'elle
que
- ils → qu'ils

Reason: it avoids a clash of vowel sounds and makes the phrase smoother to pronounce.

Meaning doesn’t change; que and qu' are the same word; the apostrophe simply shows that the e in que has been dropped.

Why is the negation split as ne croit pas instead of putting ne pas before the verb?

Standard French negation usually wraps around the main verb:

ne
- verb
  - pas

So:

Elle croit. → Elle ne croit pas.

You don’t normally say elle ne pas croit. ne pas can appear together only in special constructions, for example before an infinitive:

Elle préfère ne pas croire cette histoire. – She prefers not to believe that story.

But when the verb is conjugated, the pattern is ne + verb + pas (except with some other negative words like jamais, rien, etc., which replace pas).

Is ne really necessary? I often hear French people say things like Elle croit pas.

In informal spoken French, it’s extremely common to drop the “ne”:

Elle ne croit pas → Elle croit pas
Je n’ai pas compris → J’ai pas compris

However:

In standard written French, and in formal speech, you should keep both parts: ne … pas.
In exams, essays, and careful writing, omitting ne is considered incorrect or too informal.

So:

Your sentence in informal speech:
- Elle est nerveuse parce qu'elle croit pas qu'ils aient compris la nouvelle loi.
In correct written / neutral French, you keep ne as in the original.

Why is it la nouvelle loi and not something like le nouveau loi?

Several points here:

Gender of “loi”
- loi is feminine in French: une loi, la loi.
- So the adjective and article must be feminine too:
  - la loi, une loi, cette loi.
Form of the adjective “nouveau”
- masculine singular: nouveau
- feminine singular: nouvelle
- masculine plural: nouveaux
- feminine plural: nouvelles
Since loi is feminine singular, we use nouvelle → la nouvelle loi.
Position of the adjective
- Many adjectives normally follow the noun, but some frequent ones go before the noun.
- nouveau / nouvelle is one of those:
  - une nouvelle loi (normal)
  - une loi importante (adjective after the noun).

So la nouvelle loi is the only correct form here.

Could we use car or puisque instead of parce que here?

Yes, but the nuance changes slightly:

parce que – neutral “because”, used in most contexts:
- Elle est nerveuse parce qu'elle ne croit pas…
car – more formal / written, often explains a reason in a more “logical” or explanatory tone:
- Elle est nerveuse, car elle ne croit pas qu'ils aient compris la nouvelle loi.
- Typically used more in writing than in everyday speech.
puisque – “since / given that”, used when the reason is already known or obvious to the listener:
- Elle est nerveuse puisqu'elle ne croit pas qu'ils aient compris la nouvelle loi.
- Implies as you know, she doesn’t think they understood it.

In most neutral contexts, parce que is the safest and most natural choice.

What’s the difference between loi and règle? Could we say la nouvelle règle instead?

loi = law in the legal / governmental sense.
- Passed by a parliament, written in a legal code, etc.
règle = rule in a broader sense:
- a rule in a game, a classroom rule, company policy, a social rule, grammar rules, etc.

You could say la nouvelle règle if the context is not a formal state law but, for example, a new rule at work, at school, in a club, etc.

In a legal context (government passing a law), la nouvelle loi is the correct and more precise choice.

How is aient compris pronounced? Are any letters silent?

Pronunciation details:

aient
- Pronounced roughly like “è” ([ɛ]) in French.
- The -ent ending is silent in third-person plural verb forms.
- So aient sounds like [ɛ], similar to ait.
compris
- com- like “kohn” (nasal on [ɔ̃])
- -pris like “pree” [pri]
- Final -s is silent.

Together: aient compris ≈ [ɛ kɔ̃pri].

In the full phrase qu'ils aient compris, there is usually a liaison:

qu'ils aient → you hear a [z] sound linking qu'ils and aient: [kil zɛ].