Au réveillon, nous restons à table et nous parlons doucement.

Le réveillon is a special festive meal or evening celebration connected with a major holiday, especially Christmas Eve or New Year’s Eve in French-speaking cultures.

So Au réveillon does not just mean at night or at dinner in a general sense. It refers to that particular holiday gathering.

Because au = à + le.

Here, réveillon is a masculine singular noun: le réveillon.
When à comes before le, French contracts them:

• à + le = au
• à + les = aux

So:

• au réveillon = at the réveillon

The phrase Au réveillon is a time expression placed at the beginning of the sentence. The comma helps mark it off, much like in English when you begin with something like At Christmas dinner, ...

It is mainly a punctuation/style choice to make the sentence easier to read. In many cases, French could also omit the comma, but with a fronted time phrase, the comma is very natural.

The verb rester means to stay, to remain, or to keep being in a place/state.

So:

• nous restons à table = we stay at the table / we remain seated at the table

French uses rester because the idea is not simply we are at the table, but we continue to be there.

À table literally means at the table, but in context it often means seated at the table for a meal.

So rester à table means:

• to stay sitting at the table
• to remain at the table after or during the meal

It is a very natural expression in French.

French usually repeats the subject pronoun before each conjugated verb in normal speech and standard writing.

So nous restons à table et nous parlons doucement is the most natural standard form.

You may sometimes see:

• Nous restons à table et parlons doucement

but that is more compressed and feels more formal, literary, or less common in everyday usage.

For learners, repeating nous is the safest and most natural choice.

Doucement is an adverb, and in French adverbs often come after the conjugated verb, especially in simple tenses.

So:

• nous parlons doucement = we speak softly/quietly

This word order is very normal in French.

Doucement can mean different things depending on context, including:

• softly
• gently
• quietly
• slowly

With parler, it usually means softly or quietly.

So here nous parlons doucement means that the speakers are talking in a low, gentle voice, not that they are speaking slowly.

The present tense in French can describe:

• a habit
• something generally true
• a scene being described vividly
• something happening now

Here, it most naturally sounds like a description of what people do during the celebration:

• At the réveillon, we stay at the table and speak quietly.

So it can express a usual custom or a scene being narrated in a simple, natural way.

Both are nous forms in the present tense.

For regular -er verbs like parler, the nous ending is -ons:

• nous parlons

Rester is also an -er verb:

• je reste
• tu restes
• il/elle reste
• nous restons
• vous restez
• ils/elles restent

So the -ons ending tells you the subject is nous.

It is pronounced approximately like ray-vay-yon.

A few points that matter:

• ré sounds like ray
• vei also sounds like vay
• llon here gives a y sound before the final nasal vowel, so it is not pronounced like an English l
• the ending is nasal, somewhat like yon

A rough English-friendly guide is:

• réveillon → ray-vay-YON

Yes. In everyday spoken French, people very often use on instead of nous for we.

So a more conversational version could be:

• Au réveillon, on reste à table et on parle doucement.

That sounds very natural in spoken French.

The sentence with nous is still completely correct; it is just a bit more formal or careful.