Notre destination finale est Lille, mais une passagère pense d’abord que le train va à Paris.

Notre means our and is a possessive adjective, so it goes directly before the noun: notre destination.

• notre = our (used with a singular noun)
• nos = our (used with a plural noun)

So:

• notre destination = our destination
• nos destinations = our destinations

You do not add la before notre here. In French, possessive adjectives already do the job of my, your, our, etc.

In French, most adjectives come after the noun, so destination finale is the normal order.

• destination = destination
• finale = final

So French says literally destination final rather than final destination.

Also, finale has an -e because it agrees with destination, which is feminine:

• un arrêt final
• une destination finale

Because destination is a feminine noun, and adjectives usually agree in gender and number with the noun they describe.

Here:

• destination = feminine singular
• so final becomes finale

Compare:

• un arrêt final = a final stop
• une destination finale = a final destination

Most city names in French do not take an article when used after être or with prepositions like à.

So:

• C’est Lille
• Le train va à Lille
• Nous sommes à Paris

That is why the sentence says Notre destination finale est Lille, not est la Lille.

Une passagère means a female passenger.

French nouns often show gender:

• un passager = a male passenger / a passenger (masculine form)
• une passagère = a female passenger

The ending changes in the feminine form:

• passager → passagère

So the sentence specifically tells us the passenger is female.

The accent in passagère helps show the pronunciation and is part of the correct spelling.

• passager is pronounced with a more neutral ending
• passagère has the è sound, like eh

This often happens in feminine forms of some adjectives and nouns:

• cher → chère
• premier → première
• passager → passagère

D’abord means at first, first, or initially.

In this sentence:

• une passagère pense d’abord que... means
• a passenger first thinks that... or more naturally
• a passenger initially thinks that...

It shows that this is her first impression, and it may change later.

It is a shortened form of de abord, which in modern French is always written d’abord.

French often uses apostrophes when a vowel is dropped before another vowel:

• le ami → l’ami
• je ai → j’ai
• de abord → d’abord

You should just learn d’abord as a fixed expression.

After verbs like penser (to think), French usually uses que to introduce a full clause.

So:

• Elle pense que le train va à Paris. = She thinks that the train is going to Paris.

This works much like English that, although in English that is often omitted:

• She thinks the train is going to Paris.

In French, que is normally kept.

Yes, va is the present tense of aller (to go), and here it means goes or is going.

French often uses the simple present where English might use either:

• the train goes to Paris
• the train is going to Paris

So:

• le train va à Paris can mean the train goes to Paris or the train is going to Paris, depending on context.

In this sentence, it means the passenger thinks the train’s destination is Paris.

With aller for going to a place, French normally uses à before cities.

• aller à Paris
• aller à Lille
• aller à Londres

Pour can sometimes mean for or toward, but with a normal destination, aller à is the standard choice.

So le train va à Paris is the natural way to say the train is going to Paris.

French often uses the present tense for current movement, scheduled events, and near-future meaning.

So le train va à Paris is perfectly normal for:

• the train goes to Paris
• the train is going to Paris
• the train is headed to Paris

This is similar to English:

• The train leaves at 8.
• The train is going to Paris.

You do not need a future tense here.

Yes, sometimes, but the nuance changes a little.

• penser que = to think that
• croire que = to believe that

In many everyday contexts they are close:

• Elle pense que le train va à Paris.
• Elle croit que le train va à Paris.

But croire can sound a bit more like believe, while penser is often the more neutral choice for think.

Yes. Mais means but and connects two contrasting ideas:

• Notre destination finale est Lille
• mais une passagère pense d’abord que le train va à Paris

So the contrast is:

• the real destination is Lille,
• but the passenger initially thinks it is Paris.

You would change the noun and any agreeing words as needed.

• un passager pense d’abord... = a male passenger first thinks...
• des passagers pensent d’abord... = passengers first think...
• des passagères pensent d’abord... = female passengers first think...

Notice the verb changes too with a plural subject:

• une passagère pense
• des passagers pensent