Ce tissu est plus doux que celui de mon vieux gilet.

Because celui stands for the one or that one.

In this sentence, the comparison is really between two fabrics/materials, not between a fabric and a whole cardigan. So French uses:

• Ce tissu est plus doux que celui de mon vieux gilet.

Literally:

• This fabric is softer than the one from my old cardigan.

Here, celui replaces le tissu or le matériau belonging to the cardigan.

If you said plus doux que mon vieux gilet, it would sound like you were comparing the fabric directly to the entire cardigan, which is less precise.

Celui is a demonstrative pronoun. It means the one or that one.

French often uses demonstrative pronouns to avoid repeating a noun. In this sentence:

• Ce tissu = this fabric
• celui de mon vieux gilet = the one from my old cardigan

So celui replaces a masculine singular noun, understood here as tissu or matériau.

Related forms are:

• celui = masculine singular
• celle = feminine singular
• ceux = masculine plural
• celles = feminine plural

This is the normal French pattern for a comparison of superiority:

• plus + adjective + que = more/ -er ... than

So:

• plus doux = softer / more soft
• que = than

Examples:

• Ce pull est plus chaud que celui-ci. = This sweater is warmer than this one.
• Cette couverture est plus légère que l’autre. = This blanket is lighter than the other one.

So plus doux que means softer than.

Because it agrees with tissu, which is a masculine singular noun.

• un tissu doux
• une couverture douce

In the sentence:

• Ce tissu est plus doux...

The subject is Ce tissu, so the adjective must be masculine singular: doux.

If the noun were feminine, you would use douce:

• Cette matière est plus douce...

Because tissu is a masculine singular noun that begins with a consonant sound.

French uses:

• ce before masculine singular nouns beginning with a consonant
• cet before masculine singular nouns beginning with a vowel or mute h
• cette before feminine singular nouns

So:

• ce tissu
• cet arbre
• cet homme
• cette chemise

Since tissu starts with t, the correct form is ce.

It means of/from my old cardigan.

Here, de links celui to the cardigan it belongs to. In natural English, we often translate it as:

• the one from my old cardigan
• the one in my old cardigan
• the fabric of my old cardigan

So de is showing a relationship of possession or origin.

Because vieux is one of the common French adjectives that usually come before the noun.

Most French adjectives come after the noun, but some very common ones often come before it, especially adjectives of:

• beauty
• age
• goodness
• size

A useful memory aid is BAGS.

Since vieux means old (an age adjective), it usually goes before the noun:

• un vieux gilet
• une vieille maison

So:

• mon vieux gilet = my old cardigan

Both are masculine singular forms, but they are used in different sound environments.

• vieux is used before most masculine singular nouns:
  • un vieux gilet
• vieil is used before a masculine singular noun beginning with a vowel or mute h:
  • un vieil homme
  • un vieil appartement

Since gilet begins with a consonant sound, vieux is correct.

They are related, but they do different jobs.

• ce is a demonstrative adjective: it goes before a noun
  
  • ce tissu = this fabric
• celui is a demonstrative pronoun: it replaces a noun
  
  • celui de mon vieux gilet = the one from my old cardigan

So:

• ce needs a noun after it
• celui stands on its own, often followed by extra information such as de..., qui..., or que...

Yes. Doux can have several related meanings depending on context, such as:

• soft
• gentle
• mild
• sweet (in some contexts)

In this sentence, because we are talking about fabric, doux clearly means soft to the touch.

Examples in other contexts:

• une voix douce = a gentle/soft voice
• un climat doux = a mild climate

In this sentence, plus in plus doux is usually pronounced plu, without the final s sound.

So:

• plus doux sounds roughly like ploo doo

But pronunciation of plus can vary depending on context and speech style. For learners, the safest rule is:

• in comparisons like plus grand, plus doux, the final s is often silent

Also, que links smoothly to the next word:

• plus doux que celui...

Not quite. In modern French, gilet often refers to a cardigan, vest, or similar sleeveless/knitted garment depending on context.

In English, gilet usually means a sleeveless jacket or bodywarmer in some varieties of English, especially British English. So the exact translation depends on context.

In your sentence, if the meaning shown to the learner is cardigan, that is perfectly natural.

Yes, that would be possible in some contexts, but it is less elegant because it repeats the idea more explicitly.

For example:

• Ce tissu est plus doux que la matière de mon vieux gilet.

This is understandable, but celui de mon vieux gilet sounds more natural because French often avoids repeating the noun when it is already clear.

So the original sentence is a more idiomatic way to say it.