Cette étiquette rouge indique que le carton est fragile.

Cette means this.

It is the feminine singular form of the demonstrative adjective:

• ce = this/that before most masculine singular nouns
• cet = this/that before a masculine singular noun starting with a vowel or silent h
• cette = this/that before a feminine singular noun
• ces = these/those for plural nouns

Here, étiquette is a feminine singular noun, so French uses cette:

• cette étiquette = this label

French demonstratives can mean either this or that depending on context.

Because étiquette is feminine, and cet is only used with masculine singular nouns before a vowel or silent h.

So:

• cet arbre = this tree
• cet homme = this man
• cette étiquette = this label

Even though étiquette begins with a vowel, its gender is still feminine, so cette is the correct form.

In French, most adjectives come after the noun.

So:

• une étiquette rouge = a red label
• un carton fragile = a fragile box/carton

This is different from English, where adjectives usually come before the noun.

A few common French adjectives often go before the noun, but rouge is not one of them.

It actually agrees with étiquette, but the feminine singular form of rouge is spelled the same as the masculine singular form.

Since étiquette is feminine singular, rouge must also be feminine singular. The reason you do not see a change is simply that the spelling stays the same:

• masculine singular: rouge
• feminine singular: rouge
• masculine plural: rouges
• feminine plural: rouges

So the agreement is there, but it is invisible in the singular.

Indique comes from the verb indiquer, which means to indicate, to show, or to signal.

Here it is the third person singular present tense form:

• j’indique = I indicate
• tu indiques = you indicate
• il/elle/on indique = he/she/it/one indicates

So:

• Cette étiquette rouge indique... = This red label indicates...

In this sentence, indique is being used much like shows or means in English.

Que here means that and introduces a new clause.

So the structure is:

• Cette étiquette rouge indique = This red label indicates
• que le carton est fragile = that the box/carton is fragile

In English, that is sometimes optional:

• This red label indicates that the box is fragile.
• This red label indicates the box is fragile.

In French, que is normally required in this kind of sentence.

Le is the definite article, meaning the.

So:

• le carton = the box / the carton
• un carton = a box / a carton

French often uses the definite article where English might also use the. In this sentence, it refers to a specific box being discussed, so le carton is natural.

Not usually in the same way.

In French, carton often means:

• box
• cardboard box
• sometimes cardboard

So in this sentence, le carton most likely means the box or the cardboard box, not the English word carton as in a milk carton or juice carton.

That is an important false-friend warning: French carton and English carton overlap a little, but they are not used in exactly the same way.

Because fragile is an adjective, and after être (to be), French uses the adjective directly.

So:

• le carton est fragile = the box is fragile

You do not add an article before the adjective:

• correct: Il est fragile
• incorrect: Il est un fragile

And fragile is not a past participle here. It is simply the adjective fragile.

Yes. Adjectives in French usually agree with the noun they describe.

Here, carton is masculine singular, so fragile is also masculine singular.

Just like rouge, fragile has the same spelling in masculine and feminine singular:

• masculine singular: fragile
• feminine singular: fragile
• masculine plural: fragiles
• feminine plural: fragiles

So again, the agreement exists even though you cannot see a spelling change in the singular.

The structure is:

Cette étiquette rouge | indique | que le carton est fragile
subject | verb | subordinate clause

More specifically:

• Cette étiquette rouge = subject
• indique = main verb
• que le carton est fragile = content clause introduced by que

Inside the second clause:

• le carton = subject
• est = verb
• fragile = adjective/complement

So French is following a fairly familiar word order here: subject + verb + clause.

A simple pronunciation guide is:

set eh-tee-ket roozh an-deek kuh luh kar-ton eh fra-zheel

A few useful notes:

• cette sounds like set
• étiquette is roughly eh-tee-ket
• rouge has the French j sound, like the s in measure
• indique ends with a k sound
• que here is pronounced roughly kuh
• fragile in French sounds more like fra-zheel, not exactly like English fragile

Depending on accent and speed, some vowels may sound slightly different, but this is a good approximate guide.

Yes, possibly, but the meaning changes slightly.

• indique que = indicates that / shows that / signals that
• veut dire que = means that

In this context, indique que is very natural because a label is giving information or signaling something.

So:

• Cette étiquette rouge indique que le carton est fragile.
  = This red label indicates that the box is fragile.

Using veut dire is possible in some contexts, but indique sounds more precise and natural for a label or sign.