Learn Hardcore French: Nous sommes contents que la voiture soit enfin arrivée au garage. - We are happy that the car has finally arrived at the garage.

Because the verb in that clause is in the subjunctive mood. In French, many expressions of emotion, opinion, doubt, etc., followed by que require the subjunctive:

être content que
être triste que
avoir peur que, etc.

Here, nous sommes contents que ... triggers the subjunctive in the subordinate clause, so instead of the indicative est, you must use the present subjunctive form soit (3rd person singular of être).

If there were no expression of emotion, you would use the indicative:

Je sais que la voiture est arrivée.

What exactly is the subjunctive expressing in this sentence?

The subjunctive here signals that the clause que la voiture soit enfin arrivée au garage is not just a neutral statement of fact, but something viewed through the speakers’ emotion.

The fact: La voiture est enfin arrivée au garage.
The emotional reaction: Nous sommes contents que la voiture soit enfin arrivée au garage.

French uses the subjunctive to show that this second clause is dependent on, and coloured by, the speakers’ feeling (being happy), rather than being presented as a bare factual assertion.

What tense is soit arrivée, and how is it formed?

Soit arrivée is the past subjunctive (French: subjonctif passé).

It is formed like other compound tenses:

auxiliary in the present subjunctive (soit, from être)
past participle (arrivée, from arriver)

Pattern: que + subject + soit / ait + past participle

Examples:

Je suis content qu’il soit venu.
Nous sommes tristes qu’elle ait perdu.

The past subjunctive is used because the arrival of the car is a completed action relative to the present emotion.

Why does arrivée have an e at the end?

Because with the auxiliary être, the past participle agrees in gender and number with the subject of the verb.

Subject of arriver: la voiture (feminine singular)
Auxiliary: être (soit)
Past participle of arriver must agree: arrivé → arrivée

Other examples:

La voiture est arrivée. (fem. sg.)
Les voitures sont arrivées. (fem. pl.)
Le train est arrivé. (masc. sg.)
Les trains sont arrivés. (masc. pl.)

So here, arrivée has a final -e to match la voiture.

Why is it contents and not content in Nous sommes contents?

Adjectives in French agree with the noun or pronoun they describe in gender and number.

Subject: nous (we) → plural
Adjective: content → must be plural: contents

Some variations:

Mixed or all-male group: Nous sommes contents.
All-female group: Nous sommes contentes.
One man: Je suis content.
One woman: Je suis contente.

The -s on contents shows that nous refers to more than one person.

Could we use heureux instead of contents here, and would the meaning change?

Yes, you can say:

Nous sommes heureux que la voiture soit enfin arrivée au garage.

The difference is nuance:

content: glad, satisfied, pleased; everyday, fairly neutral.
heureux: (very) happy, delighted; a bit stronger, and sometimes slightly more formal.

In many contexts they are interchangeable, but contents sounds very natural and slightly less intense than heureux.

Remember the agreements:

Mixed / all-male group: heureux
All-female group: heureuses
Nous sommes heureuses que la voiture soit enfin arrivée.

Why do we say que after contents, and not de plus an infinitive?

You use que + subjunctive here because the subject of the main clause and the subject of the subordinate clause are different:

Main clause subject: nous (we are happy)
Subordinate clause subject: la voiture (the car arrives)

When the subjects are different, French normally uses:

être content que + subjunctive

If the subject were the same, you would usually use de + infinitive instead of que + subjunctive:

Je suis content d’être enfin arrivé au garage.
(same subject: je / être arrivé)

So:

Different subject → Je suis content que tu viennes.
Same subject → Je suis content de venir.

In your sentence, the car is not the same as nous, so que + subjunctive is required.

Why is it au garage and not à le garage or dans le garage?

Two points:

Contraction

In French, à + le always contracts to au. À le garage is simply not allowed; the correct form is au garage.

Meaning: au vs dans

au garage: to the garage / at the garage (destination or location, more general)
dans le garage: in the garage (physically inside the garage)

Your sentence:

La voiture est arrivée au garage.
→ The car has arrived at the garage (it reached the place, maybe at the entrance, in the forecourt, or inside; it’s not specified).

If you wanted to emphasise that it is physically inside the building, you could say:

La voiture est enfin arrivée dans le garage.

Can enfin go in another position, and would that change the meaning?

Here enfin means finally / at last, expressing relief.

Most natural positions are:

que la voiture soit enfin arrivée au garage (very natural)
que la voiture soit arrivée enfin au garage (possible, slightly more emphatic or oral)
que la voiture soit arrivée au garage enfin (possible, but usually with strong emphasis at the end in speech)

Putting enfin before la voiture (que enfin la voiture soit arrivée) is not natural here.

Changing the position can slightly change the rhythm or emphasis, but the basic meaning (finally / at last) stays the same.

Could we say Nous sommes contents que la voiture est enfin arrivée au garage, or is that wrong?

In standard French, that is considered incorrect. After être content que, you are expected to use the subjunctive:

Nous sommes contents que la voiture soit enfin arrivée au garage. ✅

Using the indicative (que la voiture est arrivée) after this kind of emotion verb is a common feature of very informal or non‑standard speech, but it is not accepted in careful written or formal spoken French.

So for correct, standard French, you should always use soit arrivée in this sentence, not est arrivée.