Learn Hardcore French: Je monte au grenier pour chercher une vieille couverture. - I go up to the attic to look for an old blanket.

Not usually with monter. The idiomatic collocation is monter au grenier (go up to the attic). Dans le grenier focuses on being inside the attic: Je suis dans le grenier or Il y a des cartons dans le grenier. You might hear aller dans le grenier, but with monter, stick to au.

What exactly does je monte mean here—“go upstairs” or “climb”?

Here it means “I’m going up (upstairs),” i.e., moving to a higher floor. Monter is intransitive when there’s no direct object. With a direct object, it can mean “to take/bring something up” or “to climb” something: Je monte la valise (I carry the suitcase up), Je monte l’échelle (I climb the ladder).

Can I drop pour and say Je monte au grenier chercher…?

Yes. After a motion verb (like monter, aller, descendre), French often omits pour before an infinitive of purpose: Je monte au grenier chercher… is very natural. Both versions are correct.

What about pour aller chercher or aller chercher?

Je monte au grenier pour chercher… = I’m going up in order to look for…
Je monte au grenier pour aller chercher… = I’m going up in order to go and get/fetch… (slightly stronger idea of retrieving something you expect to find)
Without pour, Je monte au grenier aller chercher… is not idiomatic. Keep pour if your infinitive is aller.
You can also say Je vais au grenier chercher… (very common).

Why is there no preposition after chercher (why not chercher pour)?

In French, chercher directly takes its object: chercher quelque chose. Do not add pour. Examples: Je cherche mes clés, Nous cherchons un restaurant.

Why does vieille come before couverture?

Some common adjectives go before the noun in French, notably those of Beauty, Age, Number, Goodness, and Size. Vieille (Age) precedes the noun: une vieille couverture. Many other adjectives normally follow the noun.

Is vieil ever used here? Why not vieil couverture?

No. Vieil is the masculine form used before a vowel or mute h: un vieil ami, un vieil arbre. Since couverture is feminine, you need vieille: une vieille couverture. Forms:

Masculine: vieux; before vowel/h: vieil
Feminine: vieille
Plural: vieux (m.), vieilles (f.)

Why une and not la?

Une is an indefinite article: you’re not specifying which blanket, just any old blanket. Use la only if a specific blanket is known to both speaker and listener: Je monte au grenier pour chercher la vieille couverture en laine (that particular one).

How would this work in the past? Which auxiliary does monter take?

It depends on transitivity:

Intransitive (no direct object): Je suis monté(e) au grenier (I went up to the attic).
Transitive (with a direct object): J’ai monté la couverture (I took the blanket up). With être, the past participle agrees with the subject; with avoir, it agrees with a preceding direct object if there is one.

Can monter be transitive in this context?

Yes, if you’re carrying something up: Je monte une couverture au grenier (I’m taking a blanket up to the attic). In the original sentence, monter is intransitive because there’s no direct object after it.

Pronunciation tips for the sentence?

You may or may not make the liaison in monte au; careful speech often links the t: [mɔ̃t‿o], everyday speech often doesn’t.
grenier ≈ [gʁə.nje]
vieille ≈ [vjɛj]
couverture ≈ [ku.vɛʁ.tyʁ]

Could I say Je monte à l’étage instead of au grenier?

Yes, but it doesn’t mean the same place. À l’étage means “upstairs/on the (next) floor,” not necessarily the attic. Au grenier specifically means the attic space under the roof.

What’s the difference between chercher, trouver, and aller chercher?

chercher = to look for (search), outcome unknown.
trouver = to find (successful result).
aller chercher = to go and get/fetch (you expect to obtain it).
So in your sentence, chercher is the best default; use aller chercher if you’re going to retrieve a known item.

Can I replace au grenier with y later?

Yes. Y stands for a previously mentioned place introduced by à. Example: — Où vas-tu ? — J’y monte pour chercher une vieille couverture.
Here, y = au grenier.

Is there anything to avoid like saying monter en haut?

Yes. Avoid pleonasms such as monter en haut or descendre en bas (they’re redundant). Just say monter or descendre.