Même après la tempête, un arc-en-ciel peut faire sourire les enfants.

Here même means even, not same.

So:

• même après la tempête = even after the storm

French même can have different uses:

• le même livre = the same book
• même après... = even after...
• moi-même = myself

In this sentence, it adds emphasis: despite the storm having happened, a rainbow can still make children smile.

Après is the normal French preposition for after.

So:

• après la tempête = after the storm

A few details:

• après is followed here by a noun phrase: la tempête
• la means the
• tempête means storm

This part is very direct and idiomatic. French often works just like English here.

The comma separates an introductory phrase from the main clause.

Structure:

• Même après la tempête, = introductory idea
• un arc-en-ciel peut faire sourire les enfants. = main statement

English does the same thing quite often:

• Even after the storm, a rainbow can make children smile.

The comma helps readability, but the meaning would still be clear without it in many cases.

Un arc-en-ciel means a rainbow.

It is a fixed compound noun:

• arc = arch / bow
• en = in
• ciel = sky

So historically it is something like an arch in the sky.

It is written with hyphens because it is treated as one expression: arc-en-ciel.

Un means a or an, so it introduces a rainbow in a general sense.

• un arc-en-ciel = a rainbow
• l’arc-en-ciel = the rainbow

Here the sentence is making a general statement: any rainbow can have that effect. It is not talking about one specific rainbow already identified, so un is natural.

Peut means can.

It comes from the verb pouvoir = to be able to / can.

Here it is the il/elle/on form in the present tense, matching un arc-en-ciel, which is singular:

• un arc-en-ciel peut = a rainbow can

A quick mini-pattern:

• je peux = I can
• tu peux = you can
• il/elle peut = he/she/it can
• nous pouvons = we can

Faire + infinitive is a very common French structure meaning to make someone do something or to cause something to happen.

So:

• faire sourire = to make smile
• faire rire = to make laugh
• faire réfléchir = to make think

In this sentence:

• un arc-en-ciel peut faire sourire les enfants
• literally: a rainbow can make the children smile

This is completely natural French.

Because after faire, French normally uses the infinitive.

So:

• faire sourire = to make smile
• not faire sourit

Compare:

• Il sourit. = He is smiling / He smiles.
• Cela le fait sourire. = That makes him smile.

After a conjugated verb like peut, and then faire, the next verb stays in the infinitive:

• peut faire sourire

Because les enfants is the direct object of faire sourire.

The idea is:

• make whom smile? → the children

So French says:

• faire sourire les enfants

not:

• faire sourire aux enfants

A helpful comparison:

• faire rire quelqu’un = make someone laugh
• faire pleurer quelqu’un = make someone cry
• faire sourire quelqu’un = make someone smile

So the person affected is usually a direct object here.

It can often sound more general in French than the children does in English.

French uses the definite article much more often than English, including for general statements.

So depending on context, les enfants could mean:

• the children (specific children already understood from context)
• or children in a broader, more generic sense

In this sentence, many learners would understand it as something like children in general, even though French uses les.

Yes, the word order is normal, and yes, you could also begin with Un arc-en-ciel.

The given sentence starts with the time/circumstance phrase for emphasis:

• Même après la tempête, un arc-en-ciel peut faire sourire les enfants.

A more neutral order would be:

• Un arc-en-ciel peut faire sourire les enfants même après la tempête.

Both are grammatical, but the original version puts focus first on the contrast: even after the storm.

It is pronounced approximately like:

• ark-ahn-syel

A more careful breakdown:

• arc → sounds like ark
• en → a nasal vowel, roughly ahn
• ciel → roughly syel

Also, in normal speech there is a linking effect between arc and en, so it flows smoothly as one unit.

Yes. That is often a very natural English translation.

So:

• un arc-en-ciel peut faire sourire les enfants
• can be understood as:
  • a rainbow can make children smile
  • a rainbow can bring a smile to children’s faces

The French structure is literal with faire sourire, but in English you can translate it in a slightly more natural or expressive way depending on context.