J’attends, non pas que Paul refuse, mais pour vérifier.

It means something like not or not so much ... as ..., and in the pattern non pas ..., mais ..., it sets up a correction or contrast: not X, but Y.

With non pas que, the sense becomes not that .... This is a fairly formal or literary way to reject one explanation before giving the real one.

Because non pas que is a fixed pattern meaning not that ....

So:

• non pas que Paul refuse = not that Paul refuses / not that Paul would refuse

This is different from:

• non pas parce que Paul refuse = not because Paul refuses

That difference matters here. Que introduces a clause of the type not that ..., while parce que introduces a reason because ....

Yes. After non pas que, French normally uses the subjunctive.

So in non pas que Paul refuse, the verb is understood as subjunctive. The tricky part is that for refuser, the 3rd person singular subjunctive and indicative have the same form:

• indicative: il refuse
• subjunctive: qu’il refuse

So you can only tell from the structure, not from the spelling.

As written, it sounds awkward to most speakers.

The main issue is that the two parts of non pas ..., mais ... do not match very well:

• que Paul refuse = a full clause
• pour vérifier = an infinitive phrase expressing purpose

French usually prefers those two sides to be more parallel.

More natural possibilities would be:

• J’attends, non pas parce que Paul refuse, mais pour vérifier.
• J’attends, non pas que Paul refuse, mais parce que je veux vérifier.

So the original sentence is useful for studying pieces of grammar, but stylistically it is not the best model.

Because the sentence mixes two different kinds of structure.

• non pas que Paul refuse = not that Paul refuses / not that Paul would refuse
• pour vérifier = to check / in order to check

French often sounds better when the contrast after non pas ..., mais ... is balanced.

So if the first part is non pas que + clause, the second part is often another clause, for example:

• mais parce que je veux vérifier

If you want to keep pour vérifier, then the first part is often better as:

• non pas parce que Paul refuse

That gives a more even contrast:

• not because Paul refuses, but to check

They are close, but not identical.

• non pas que ... = not that ...
• non pas parce que ... = not because ...

Non pas que ... often sounds a little more nuanced or formal. It can suggest: I’m not saying that ... or it’s not as if ...

Example:

• Je pars tôt, non pas que je sois fatigué, mais parce que j’ai un rendez-vous. = I’m leaving early, not because I’m tired, but because I have an appointment.

In your sentence, many learners expect parce que, because the second half pour vérifier sounds like it is contrasting reasons or purposes, not contrasting with a not that ... clause.

Usually, attendre means to wait.

So J’attends by itself normally means I’m waiting or I wait.

English speakers often confuse attendre with to expect, but French usually uses another structure for that idea, often s’attendre à.

So:

• J’attends Paul = I’m waiting for Paul
• Je m’attends à un refus = I expect a refusal

That is a very common false-friend issue.

The commas mark non pas ..., mais ... as a kind of inserted contrast or parenthetical comment.

Without getting too technical, the writer is pausing to say:

• I’m waiting — not that Paul refuses — but to check

In formal writing, commas often help show that kind of interruption or correction. Punctuation can vary a little, but the commas here are understandable.

Because je becomes j’ before a vowel sound. This is called elision.

So:

• je attends → j’attends

You will see this all the time in French:

• j’aime
• j’habite
• j’écoute

It is purely a pronunciation and spelling rule.