Je m’aperçois que j’ai oublié mon portefeuille à la maison.

Because s’apercevoir is a pronominal verb in this meaning.

• apercevoir by itself usually means something like to catch sight of or to notice
• s’apercevoir means to realize / to notice / to become aware

So:

• J’aperçois Paul. = I catch sight of Paul.
• Je m’aperçois que... = I realize that...

The me becomes m’ before a vowel:

• je me aperçois → je m’aperçois

Here, m’ does not mean myself in a literal English sense. It is just part of how this verb is used.

It means something like:

• I realize that...
• I notice that...
• It dawns on me that...

In this sentence, Je m’aperçois que j’ai oublié mon portefeuille à la maison means that the speaker suddenly becomes aware of the fact.

A very natural English translation would be:

• I realize I left my wallet at home.

Even though the French literally uses that (que), English often drops that.

Que introduces a subordinate clause. Here it means that.

• Je m’aperçois = I realize
• que j’ai oublié mon portefeuille à la maison = that I forgot my wallet at home

So the structure is:

• main clause: Je m’aperçois
• subordinate clause: que j’ai oublié...

In English, that is often optional:

• I realize that I forgot my wallet
• I realize I forgot my wallet

In French, que is normally required here.

J’ai oublié is the passé composé of oublier (to forget).

It is formed with:

• avoir in the present: j’ai
• past participle: oublié

So:

• oublier = to forget
• j’oublie = I forget / I am forgetting
• j’ai oublié = I forgot / I have forgotten

In this sentence, the forgetting happened before the realization, so French uses a past tense:

• first: you left the wallet at home
• then: you realize it

Because with avoir, the past participle usually does not agree with the subject.

So:

• j’ai oublié
• elle a oublié
• nous avons oublié

The form oublié stays the same in these cases.

Agreement with avoir only happens in special cases, mainly when a direct object comes before the verb.

That is not happening here, because mon portefeuille comes after the verb:

• j’ai oublié mon portefeuille

So oublié stays unchanged.

French often uses a possessive adjective where English also uses one:

• mon portefeuille = my wallet

This clearly shows whose wallet it is.

Using le portefeuille would mean the wallet, which is less natural here unless the context already makes it obvious which wallet you mean.

So:

• J’ai oublié mon portefeuille. = I forgot my wallet.

That is the normal way to say it.

À la maison means at home.

So:

• j’ai oublié mon portefeuille à la maison = I forgot my wallet at home

This is very close to chez moi (at my place / at my home), and in many contexts they can be similar.

But there is a slight nuance:

• à la maison focuses on home
• chez moi focuses on my place

Both can work in many everyday situations, but à la maison is extremely common for at home.

French often drops a vowel before another vowel or a silent h. This is called elision.

Here:

• me
  • aperçois → m’aperçois
• je
  • ai → j’ai

This avoids awkward vowel combinations.

So instead of saying:

• je me aperçois
• je ai oublié

French contracts them to:

• je m’aperçois
• j’ai oublié

This is required in standard French.

The ç is called c cédille. It makes the c sound like s before a, o, or u.

So in aperçois, the ending is pronounced roughly like:

• ap-er-SWA

Without the cedilla, coi would normally sound with a hard k sound, which would be wrong here.

A rough pronunciation of Je m’aperçois is:

• zhuh mah-per-SWA

And the whole sentence is roughly:

• zhuh mah-per-SWA kuh zhay oo-blee-ay mon port-fuh-yuh ah la meh-zon

That is only an approximation, but it helps with the main sounds.

Yes. Je me rends compte que... is a very common alternative and often sounds especially natural in everyday French.

Both can mean:

• I realize that...

Compare:

• Je m’aperçois que j’ai oublié mon portefeuille à la maison.
• Je me rends compte que j’ai oublié mon portefeuille à la maison.

The second one is often more common in conversation.
The first one is still perfectly correct and natural.

It is basically neutral standard French.

• Je m’aperçois que... is correct and natural
• j’ai oublié mon portefeuille à la maison is also standard everyday French

It is not especially formal, but it is not slang either.

In very casual speech, a person might choose a slightly different verb, such as:

• Je me rends compte que...

But the original sentence is completely normal and appropriate in both speech and writing.

In French, object/reflexive pronouns usually come before the verb.

So with a reflexive verb in the present tense:

• je me rends compte
• je me lève
• je m’aperçois

The pronoun goes between the subject and the verb:

• Je
  • m’
    • aperçois

English learners often want to place pronouns after the verb, but French normally does not do that in this kind of sentence.

Not naturally in this sentence.

French uses j’ai oublié because the forgetting happened before the moment of realization. That past action is important.

If you said j’oublie mon portefeuille à la maison, it would usually mean something like:

• I am forgetting my wallet at home
• or describe a habitual/repeated action, depending on context

That is not what is meant here. The speaker is talking about a completed action in the past, so j’ai oublié is the right choice.