La faïence est fragile.

Because French often uses the definite article (le / la / les) to talk about something in general.

So La faïence est fragile means something like earthenware is fragile or faience is fragile as a general statement.

If you said Une faïence est fragile, it would sound odd in most contexts, because faïence is usually being treated here as a material or category, not as one single unspecified item.

Because faïence is simply a feminine noun in French, and noun gender is something you usually have to learn with the word.

That is why it takes:

• la faïence
• elle if you refer back to it
• feminine agreement where needed

There is not always a logical reason for grammatical gender, so the best habit is to learn the noun together with its article: la faïence.

The two dots are called a diaeresis (in French, tréma).

They show that the i should be pronounced separately from the vowel before it.

So faïence is pronounced roughly like fa-ee-ans (more naturally: fa-yanss), not as if ai were one single vowel sound.

The dots help you avoid reading it as one combined vowel group.

A good English-friendly approximation is:

fa-YAHNSS

More precisely, the French pronunciation is approximately fa-yanss, with:

• fa as a short opening syllable
• ï creating a separate y-like glide
• the ending sounding nasal, roughly yanss

The final -ce gives an s sound.

A simple approximation is:

la fa-YAHNSS ay fra-ZHEEL

A bit more naturally:

• La = la
• faïence = fa-yanss
• est = eh
• fragile = fra-zheel

So the full sentence sounds roughly like:

la fa-yanss eh fra-zheel

Est is the third-person singular form of the verb être (to be).

So:

• je suis = I am
• tu es = you are
• il / elle est = he / she / it is

Here, la faïence is a singular subject, so French uses est:

La faïence est fragile = The earthenware is fragile / Earthenware is fragile

Because some French adjectives have the same form in the masculine and feminine singular.

So:

• un objet fragile
• une matière fragile

Both use fragile.

Many adjectives do change in the feminine, but fragile already has a form that works for both masculine and feminine singular. Only the article and noun show the gender clearly here.

Only if the subject were plural.

In your sentence, la faïence is singular, so the adjective stays singular too:

• La faïence est fragile.

If the subject were plural, you would use:

• Les faïences sont fragiles.

So yes, fragiles exists, but not in this sentence.

Yes, in this sentence it is very similar to English:

La faïence = subject
est = verb
fragile = adjective / description

So it follows the pattern:

Subject + verb + adjective

That is one reason this sentence feels quite straightforward for English speakers.

Not if you want a complete sentence meaning The earthenware is fragile.

French needs the verb être here, just as English needs is.

• La faïence est fragile = complete sentence
• La faïence fragile = noun phrase, meaning something like the fragile earthenware

So without est, it stops being a full statement.

Here it is being used more like a material or category word.

That is why the sentence sounds like a general fact:

• La faïence est fragile.

It is similar to how French can say:

• Le verre est fragile.
• Le métal est solide.

So in this sentence, faïence is not really pointing to one individual object, but to earthenware as a type of material or ware.

That is a very common difference between French and English.

English often says:

• Earthenware is fragile
• Wine is expensive
• Nature is beautiful

French often prefers:

• La faïence est fragile
• Le vin est cher
• La nature est belle

So even when English has no article, French often uses le / la / les to talk about things in a general sense.

In this sentence, fragile comes after the verb because it is part of the description:

• La faïence est fragile.

If you use it directly with the noun, it usually comes after the noun:

• la faïence fragile = the fragile earthenware

That is normal, because most French descriptive adjectives are placed after the noun, though there are exceptions with other adjectives.