J’ai des frissons quand j’écoute cette chanson.

In French, many physical sensations are expressed with avoir (to have), not être (to be).

So French says:

• J’ai faim = I am hungry
• J’ai peur = I am afraid
• J’ai des frissons = I have chills / I get goosebumps

Even though English often uses to be, French often uses to have in these cases.

Un frisson is a shiver, chill, or goosebump-like sensation.

So des frissons means shivers, chills, or goosebumps, depending on context.

In this sentence, it usually suggests an emotional reaction, like a song affects you so strongly that it gives you chills.

French normally uses the plural in this expression: avoir des frissons.

That is just the usual idiomatic way to say to have chills / to get goosebumps.

You may sometimes see the singular un frisson, but that often refers to a single shiver or a thrill:

• J’ai un frisson. = I feel a shiver.
• J’ai des frissons. = I have chills / I’m getting goosebumps.

Des is the plural indefinite article, meaning something like some in English.

• un frisson = a shiver
• des frissons = some shivers / chills

In English, we usually do not say I have some chills, but French naturally uses des in this expression.

Quand means when.

So:

• quand j’écoute cette chanson = when I listen to this song

It introduces the time situation in which the speaker gets chills.

French could also use lorsque, which also means when, but quand is more common and natural in everyday speech.

French avoids having je directly before a vowel sound, so it shortens je to j’. This is called elision.

Because écoute begins with a vowel sound, you must write:

• j’écoute

not:

• je écoute

The same thing happens in J’ai:

• je ai becomes j’ai

The verb is écouter (to listen to), and the forms of this verb keep the é:

• j’écoute
• tu écoutes
• il/elle écoute

The accent helps show the pronunciation.
é is pronounced like the ay sound in say (though not exactly the same).

So j’écoute is pronounced roughly like zheh-koot.

Cette means this for a feminine singular noun.

The noun chanson (song) is feminine:

• une chanson
• cette chanson = this song

Compare:

• ce livre = this book (masculine)
• cet album = this album (masculine before a vowel sound)
• cette chanson = this song (feminine)

French often uses the present tense to talk about something that happens generally, habitually, or whenever something occurs.

So:

• J’ai des frissons quand j’écoute cette chanson.

means something like:

• I get chills when I listen to this song
• Whenever I listen to this song, I get chills

It is not necessarily happening only right now. It can describe a repeated reaction.

Yes. In fact, that is probably the most natural interpretation here.

Avoir des frissons can be physical, but it is also very commonly used for an emotional reaction such as:

• being moved by music
• feeling fear
• feeling excitement
• feeling awe

So in this sentence, it likely means the song is so powerful that it gives the speaker goosebumps.

Yes, you could say:

• J’ai des frissons en écoutant cette chanson.

This means I get chills while listening to this song.

The difference is small:

• quand j’écoute cette chanson = when I listen to this song / whenever I listen to this song
• en écoutant cette chanson = while listening to this song

Both are correct, but quand j’écoute cette chanson emphasizes the repeated situation a little more clearly.

Yes. This is an important point.

In French, écouter takes a direct object, so you say:

• écouter une chanson = to listen to a song
• j’écoute cette chanson = I listen to this song

English uses listen to, but French does not use a word equivalent to to here.

So:

• J’écoute cette chanson = correct
• J’écoute à cette chanson = incorrect

A natural pronunciation is roughly:

J’ai des frissons quand j’écoute cette chanson
→ zhay day free-sohn kahn zhay-koot set shahn-sohn

A few helpful notes:

• J’ai sounds like zhay
• des frissons: the s in des is silent
• quand sounds like kahn
• j’écoute links smoothly after quand
• chanson has a nasal sound at the end, not a strong n sound like in English

Yes, but the meaning changes slightly.

• cette chanson = this song
• ce morceau = this piece / track
• cette musique = this music

If you mean one specific song with lyrics, cette chanson is perfect.
If you mean a track more generally, ce morceau also works.
If you mean the music in a broader sense, cette musique is possible too.