Après un petit malentendu avec la voisine, Marie se met à rire et lui explique la situation.

Après by itself is a preposition meaning after. It can be followed by a noun phrase, and here un petit malentendu is a noun phrase:

• après un malentendu = after a misunderstanding

You use après que when it is followed by a full clause with a verb:

• Après qu’ils ont parlé... = After they spoke...

So in this sentence, après alone is correct because what follows is a thing, not a whole clause.

Literally, petit means small, but in expressions like this it often means minor or slight.

So:

• un malentendu = a misunderstanding
• un petit malentendu = a small/minor misunderstanding

It softens the idea a bit, almost like saying it was not too serious.

Also, petit is masculine singular here because malentendu is masculine singular.

French usually uses an article where English may not. Here la voisine means the neighbor.

So:

• voisine alone would usually not work here in normal standard French
• la voisine identifies the person involved

Also, voisine is the feminine form of voisin, so it tells you the neighbor is a woman.

Avec means with, and it shows who Marie had the misunderstanding with.

• un malentendu avec quelqu’un = a misunderstanding with someone

This is a very natural way to express the relationship between the misunderstanding and the other person involved.

Se mettre à + infinitive is a very common French structure meaning to start/begin to do something.

So:

• se met à rire = starts laughing / begins to laugh

The full expression is:

• se mettre à rire = to burst out laughing / to start laughing

In context, it suggests a sudden change: after the misunderstanding, Marie starts laughing.

Because the meaning is different.

• Marie rit = Marie laughs / is laughing
• Marie se met à rire = Marie starts laughing

So se mettre à + infinitive focuses on the beginning of the action, not just the action itself.

Because se mettre in this construction is followed by à + infinitive.

This is just the pattern of the expression:

• se mettre à parler = to start talking
• se mettre à pleurer = to start crying
• se mettre à rire = to start laughing

It is something you need to learn as a set phrase.

Here lui means to her, and it refers to la voisine.

In Marie ... lui explique la situation:

• la situation = the thing being explained
• lui = the person Marie explains it to

So the structure is:

• expliquer quelque chose à quelqu’un = to explain something to someone

French replaces à la voisine with the indirect object pronoun lui.

For indirect object pronouns, French uses:

• lui = to him / to her
• leur = to them

So lui works for both masculine and feminine singular.

That is different from direct object pronouns:

• le = him/it
• la = her/it

Here the verb is expliquer quelque chose à quelqu’un, so the person is an indirect object, which is why French uses lui.

Object pronouns usually come before the conjugated verb in French.

So:

• Marie lui explique la situation = Marie explains the situation to her

That is the normal order:

• subject + pronoun + verb + noun object

Compare:

• Je lui parle
• Nous leur écrivons
• Elle lui explique la situation

It could be, but the sentence chooses not to.

The full noun phrase is:

• la situation = the situation

If you wanted to replace it with a pronoun, you could say:

• Marie la lui explique = Marie explains it to her

Here:

• la = it (the situation)
• lui = to her

But when the noun is stated explicitly, French keeps:

• lui explique la situation

The present tense can be used in French for several reasons, depending on context:

• to describe something happening now
• to tell a story more vividly
• to summarize events

So Marie se met à rire et lui explique la situation may be a normal present or a narrative present. French often uses the present this way, especially in examples, summaries, or storytelling.

Because both verbs have the same subject, Marie.

So French, like English, can coordinate the verbs:

• Marie se met à rire et lui explique la situation

This means:

• Marie starts laughing
• and Marie explains the situation

There is no need to repeat the subject unless you want emphasis or clarity.