Paul a quatre-vingts ans.

That is just how age is expressed in French: French uses avoir (to have) with age, not être (to be).

So:

• Paul a quatre-vingts ans. = Paul is eighty years old.
• literally: Paul has eighty years.

This is one of the first big differences English speakers have to memorize.

More examples:

• J’ai 20 ans. = I am 20.
• Elle a 6 ans. = She is 6.
• Nous avons 40 ans. = We are 40 years old.

No. That is not correct French.

For age, you must use avoir:

• Paul a quatre-vingts ans.

Using être for age sounds like an English-style translation rather than natural French.

This is a normal French number pattern. In standard French from France, 80 is built as:

• quatre = four
• vingt = twenty

So quatre-vingts literally means four twenties = 80.

This can feel strange to English speakers, but it is standard.

A few related numbers:

• 60 = soixante
• 70 = soixante-dix literally sixty-ten
• 80 = quatre-vingts literally four twenties
• 90 = quatre-vingt-dix literally four-twenty-ten

In some French-speaking regions, other forms such as octante or huitante may exist, but quatre-vingts is the standard form learners usually need.

The s appears in quatre-vingts when the number is exactly 80.

So:

• quatre-vingts = 80

But the s disappears when another number follows:

• quatre-vingt-un = 81
• quatre-vingt-deux = 82

A useful rule:

• 80 exactly -> quatre-vingts
• 81, 82, 83... -> quatre-vingt-... with no s

In your sentence, it is exactly 80, so quatre-vingts keeps the s.

A simple learner-friendly pronunciation is:

• katr-van-zan

A bit more carefully:

• quatre sounds roughly like katr
• vingts sounds roughly like van
• ans sounds roughly like an / ahn

Because ans begins with a vowel sound, there is a liaison, so quatre-vingts ans flows together and sounds like quatre-ving-zans.

Also:

• the final s in ans is silent
• French nasal vowels make vingts and ans sound different from normal English vowels

For age, French normally uses ans.

So you say:

• Il a dix ans.
• Elle a trente ans.
• Paul a quatre-vingts ans.

Années means years too, but it is used in other contexts, not the normal way to give someone’s age.

For example:

• J’ai passé trois années en France. = I spent three years in France.

So for age, remember:

• avoir + number + ans

Because Paul is eighty years old, and that is more than one year.

So:

• 1 year old -> un an
• 2 years old -> deux ans
• 80 years old -> quatre-vingts ans

Notice that French uses:

• an in the singular
• ans in the plural

Examples:

• Il a un an.
• Il a deux ans.

Yes. In modern written French, number words are normally linked with hyphens.

So you should write:

• quatre-vingts
• quatre-vingt-un
• soixante-dix

In your sentence, the correct spelling is:

• Paul a quatre-vingts ans.

This is something worth copying exactly, because number spelling in French is very fixed.

It is completely normal everyday French.

You can use this pattern in any situation:

• conversation
• writing
• school exercises
• formal and informal contexts

It is the standard, natural way to state someone’s age.