Nous nous occupons du jardin.

They do two different jobs.

• The first nous is the subject pronoun: we
• The second nous is a reflexive/pronominal pronoun, part of the verb s'occuper de

So:

• Nous = we
• nous occupons = take care of / deal with, in the we form

In other words, s'occuper de is a verb expression that normally needs that extra pronoun.

The basic verb is s'occuper de.

It means things like:

• to take care of
• to look after
• to deal with

So the sentence uses the present-tense nous form of s'occuper de:

• je m'occupe de
• tu t'occupes de
• il / elle / on s'occupe de
• nous nous occupons de
• vous vous occupez de
• ils / elles s'occupent de

Because s'occuper is used with de:

• s'occuper de quelque chose
• s'occuper de quelqu'un

So you do not say s'occuper le jardin.

Here, de comes before le jardin, and in French:

• de + le = du

So:

• de le jardin → du jardin

That is why the sentence is Nous nous occupons du jardin.

No. Here du is not the partitive article.

It is simply the contraction of:

• de + le = du

That happens because the verb pattern is s'occuper de.

So in this sentence, du jardin means of the garden / the garden after de, not some garden.

Occupons is the present tense.

French present tense can often match more than one English form, depending on context. So this sentence could be translated as:

• We take care of the garden
• We are taking care of the garden
• We look after the garden

French does not need a separate am/is/are + -ing form the way English often does.

Yes, it is a pronominal verb, and historically/literally it is close to to occupy oneself with.

But in normal modern French, you should learn s'occuper de as a set expression meaning:

• to take care of
• to look after
• to handle

So even if English does not use a reflexive form here, French does.

That changes the meaning a lot.

• Nous nous occupons du jardin = We take care of the garden
• Nous occupons le jardin = We occupy the garden

So the second nous and the de are important. Without them, you no longer have s'occuper de.

A careful pronunciation is roughly:

noo noo-zoh-ky-pon dy zhar-dan

A more IPA-style version is:

/nu nu.z‿ɔ.ky.pɔ̃ dy ʒaʁ.dɛ̃/

A few useful points:

• both nous are pronounced noo
• there is a liaison between the second nous and occupons, so you hear a z sound: nous occupons
• jardin ends with a nasal vowel, so the final n is not fully pronounced like an English n

Because nous does not elide.

Some French words drop a vowel before another vowel, such as:

• je → j'
• me → m'
• te → t'
• se → s'
• de → d'

But nous stays nous, even before a vowel. So:

• Nous nous occupons... is correct
• N'nous or anything similar is not possible

Yes. In everyday spoken French, on is very often used instead of nous for we.

So these are both correct:

• Nous nous occupons du jardin
• On s'occupe du jardin

The first is a bit more formal or careful. The second is very common in conversation.