Comme je suis fatigué, je vais me coucher tôt.

In this sentence, comme means since or as, and it introduces the reason.

So Comme je suis fatigué means Since I’m tired / As I’m tired.

It does not mean like here.

When comme means since/as to introduce a reason, it is very commonly placed at the beginning of the sentence.

So this is natural:

Comme je suis fatigué, je vais me coucher tôt.

If you want to put the reason later, French usually prefers parce que instead:

Je vais me coucher tôt parce que je suis fatigué.

Using comme after the main clause is much less natural in this meaning.

Because Comme je suis fatigué is an introductory clause giving the reason, and it is followed by the main clause:

• Comme je suis fatigué, = reason
• je vais me coucher tôt. = main statement

In English, you would usually do the same: Since I’m tired, I’m going to bed early.

French says to be tired, just like English.

• je suis fatigué = I am tired

You do not say j’ai fatigué for I am tired.
That would be wrong here, because fatigué is being used as an adjective.

A related expression is j’ai sommeil, which means I’m sleepy, but that is slightly different from I’m tired.

Because there are two clauses, and each one needs its own subject in French:

• Comme je suis fatigué
• je vais me coucher tôt

French usually repeats the subject pronoun much more consistently than English sometimes does. So even though both parts refer to I, you still say je in both clauses.

Se coucher is a reflexive verb that means to go to bed or more literally to lie down.

In everyday French, se coucher is the normal way to say go to bed:

• Je me couche tôt. = I go to bed early.
• Il se couche tard. = He goes to bed late.

So in your sentence, me coucher is the infinitive form linked to je: I am going to go to bed.

Because se coucher is reflexive. The reflexive pronoun changes to match the subject:

• je me couche
• tu te couches
• il/elle se couche
• nous nous couchons
• vous vous couchez
• ils/elles se couchent

With je, the reflexive pronoun is me.

So:

• se coucher = the dictionary form
• je vais me coucher = I am going to go to bed

Because the pronoun goes with the infinitive coucher, not with vais.

In the near future structure:

• aller + infinitive

if the infinitive is reflexive, the reflexive pronoun stays directly in front of that infinitive:

• je vais me coucher
• tu vas te reposer
• il va se lever

So je me vais coucher is not correct.

Je vais me coucher uses the near future: I’m going to go to bed.

It often sounds a bit more immediate or connected to a present situation.

Je me coucherai tôt is the simple future: I will go to bed early.

In many everyday situations, both are possible, but je vais me coucher often feels very natural when the decision comes from the current situation:

Comme je suis fatigué, je vais me coucher tôt.

That sounds like: Since I’m tired, I’m going to bed early.

Because adjectives in French agree with the person they describe.

If the speaker is masculine singular:

• Je suis fatigué.

If the speaker is feminine singular:

• Je suis fatiguée.

If plural, it changes again:

• Nous sommes fatigués / fatiguées

So the sentence would be written differently depending on who is speaking.

Tôt is an adverb meaning early.

It modifies se coucher:

• se coucher tôt = to go to bed early

It does not change form to agree with gender or number.

Compare:

• tôt = early
• tard = late

So:

• Je vais me coucher tôt. = I’m going to bed early.
• Je vais me coucher tard. = I’m going to bed late.