Normalement, si le train est à l'heure, j'arrive au bureau avant huit heures.

Normalement means normally, usually, or under normal circumstances.

It tells you that the sentence is describing a habit or what typically happens, not a one-time event. So the speaker is not making a guaranteed promise; they are saying what generally happens when things go as expected.

Si means if and introduces a condition:

si le train est à l'heure = if the train is on time

This is the normal French word for if in conditional sentences.

A learner might wonder about quand. Quand means when, and it suggests the event is expected rather than conditional. Here, the train being on time is a condition, so si is the correct choice.

French often uses the present tense to talk about:

• habits
• routines
• general truths
• things that usually happen

So this sentence means something like:
Normally, if the train is on time, I get to the office before eight.

That is why est and arrive are both in the present.

In French, after si meaning if, you normally do not use the future tense in the si-clause.

So French says:

• Si le train est à l'heure, j'arriverai avant huit heures.

not:

• Si le train sera à l'heure...

In your sentence, though, the whole idea is habitual, so the speaker uses present in both parts:

• si le train est à l'heure, j'arrive...

So there are really two points:

1. After si, French uses the present, not the future.
2. Because this sentence describes a routine, the main clause is also in the present.

Yes, that is grammatically possible, but it changes the feel.

• j'arrive suggests a usual result or routine.
• j'arriverai suggests a specific future result.

So:

• Normalement, si le train est à l'heure, j'arrive au bureau avant huit heures.
  = This is what usually happens.

• Normalement, si le train est à l'heure, j'arriverai au bureau avant huit heures.
  = On this particular future occasion, that is what I expect to happen.

À l'heure is an expression meaning on time.

So:

• le train est à l'heure = the train is on time

It is a fixed phrase, and it is very common in French.

Also note the form:

• à + l'heure

You get l' because heure begins with a silent h, so French treats it like a vowel sound.

French often uses the definite article (le, la, les) where English might use a possessive such as my.

So le train here can mean:

• the train
• or more naturally in context, the train I usually take

French does not always need to say mon train if the context already makes it clear which train is meant.

Au is the contraction of:

• à + le = au

So:

• au bureau = to the office / at the office, depending on context

With arriver, it means arrive at the office or get to the office.

This is just standard French contraction:

• à le bureau is not correct
• au bureau is correct

French uses elision before a vowel sound.

Since arrive begins with a vowel, je becomes j':

• j'arrive

This is the same pattern as:

• j'aime
• j'habite
• j'écoute

It helps French sound smoother.

French uses heures in the plural when telling time with numbers greater than one:

• huit heures = eight o’clock

So:

• avant huit heures = before eight o’clock

Even though English often says before eight, French commonly includes heures.

The two verbs are related, but they do not mean the same thing:

• aller au bureau = to go to the office
• arriver au bureau = to arrive at the office / to get to the office

In this sentence, the focus is on the time the speaker reaches the office, so arriver is the better choice.

The commas help organize the sentence and make it easier to read:

Normalement, si le train est à l'heure, j'arrive au bureau avant huit heures.

They mark:

• the introductory adverb Normalement
• the conditional clause si le train est à l'heure

In writing, this punctuation is very natural and standard. In speech, you would usually hear small pauses there too.