Nous resterons au café jusqu’à ce que l’averse passe.

Resterons is the simple future form of rester (to stay / remain).

• nous restons = we stay / we are staying
• nous resterons = we will stay

So Nous resterons au café... means We will stay at the café...

Au is the contraction of à + le.

• à = at / to
• le = the
• à le becomes au

So:

• au café = at the café or sometimes to the café, depending on context

Here, it means at the café.

Jusqu’à usually needs a noun or time expression after it:

• jusqu’à midi = until noon
• jusqu’à la fin = until the end

But when French says until followed by a whole clause, it often uses jusqu’à ce que:

• jusqu’à ce que l’averse passe = until the rain shower passes

So jusqu’à ce que introduces a verb clause, not just a noun.

Because jusqu’à ce que normally requires the subjunctive in French.

So:

• il passe = indicative
• qu’il passe = subjunctive
• l’averse passe here is the subjunctive form after jusqu’à ce que

This happens because French often uses the subjunctive after expressions that refer to something anticipated, uncertain, or not yet completed.

With passer, the il/elle/on form of the present indicative and present subjunctive happens to look the same:

• indicative: il passe
• subjunctive: qu’il passe

So the form itself does not change in spelling here. You know it is subjunctive because of the grammar trigger: jusqu’à ce que.

L’averse means a rain shower, downpour, or sudden burst of rain.

It is more specific than la pluie:

• la pluie = rain in general
• une averse = a short, often sudden shower of rain

So the sentence suggests they are waiting for a passing shower to stop.

Because averse begins with a vowel sound, so la becomes l’ by elision:

• la pluie
• l’averse

This is very common in French:

• l’homme
• l’école
• l’idée

Yes. That would also be natural and means something like until the rain shower stops.

There is a slight nuance:

• jusqu’à ce que l’averse passe = until the shower passes
• jusqu’à ce que l’averse s’arrête = until the shower stops

Both are good French. Passe gives the sense of the shower passing over.

In French, after jusqu’à ce que, you do not use the future. You use the subjunctive present.

So French says:

• Nous resterons au café jusqu’à ce que l’averse passe.

Not:

• ... jusqu’à ce que l’averse passera ❌

This is different from the main clause, which can be future: Nous resterons...

Usually stay sounds most natural in English here:

• Nous resterons au café... = We’ll stay at the café...

Remain is possible, but it sounds a little more formal in English:

• We’ll remain at the café...

So for most learners, stay is the best everyday translation.