Bonne année !

Because année is a feminine noun in French, and adjectives usually agree with the noun they describe.

• masculine: bon
• feminine: bonne

So:

• un bon jour would use the masculine form
• une bonne année uses the feminine form

That is why the greeting is Bonne année !

In short greetings and wishes, French often leaves out the article.

So instead of saying something like une bonne année, French naturally says:

• Bonne année !
• Bon anniversaire !
• Bonne journée !

This is just the standard idiomatic way to express a wish.

The word année has two accents:

• a in année has no accent
• the two é letters have an acute accent

The é tells you the vowel is pronounced like ay in English, but shorter and cleaner.

So année is pronounced approximately ah-nay.

The accents are part of the spelling, so you should write them: année, not annee.

A rough English approximation is:

bun ah-nay

But more accurately:

• Bonne sounds like bonn, with a short o sound and a final n that is actually pronounced
• année sounds like a-nay

In natural speech, French speakers link the words together smoothly, so it can sound a bit like:

bon ah-nay

The exact pronunciation will depend on accent, but that is a good learner-friendly starting point.

They say it to wish someone a happy new year.

It is commonly used:

• on New Year’s Day
• in the first days or weeks of January
• when seeing someone for the first time after the new year begins

It can be said to friends, family, coworkers, neighbors, and so on. It is a very normal and standard greeting for the new year.

Yes.

• Bonne année ! = the basic, common greeting
• Bonne année à toi ! = Happy New Year to you, informal
• Bonne année à vous ! = Happy New Year to you, formal or plural

The shorter Bonne année ! is very common by itself, because the person being addressed is usually obvious from context.

For most French nouns, grammatical gender is something you simply learn with the word. There is usually no logical reason from an English-speaking point of view.

You learn:

• le jour = day, masculine
• l’année = year, feminine

A useful habit is to memorize nouns with their article:

• une année
• l’année

That helps you remember that the correct adjective form is bonne.

Yes, both can mean year, but they are not always used in the same way.

French has both:

• an
• année

Very roughly:

• an is often used for counting years or stating age/number
• année often emphasizes the duration or the year as a stretch of time

In this greeting, French uses année, not an:

• Bonne année ! is correct
• Bon an ! is old-fashioned and not what learners should normally use

So for the New Year greeting, just remember Bonne année !

Because this is a greeting or wish, and French often writes these with an exclamation mark:

• Bonjour !
• Bonsoir !
• Bonne chance !
• Bonne année !

It shows warmth and friendliness. In casual writing, especially messages or cards, the exclamation mark is very common.

Yes. It works in both.

You can say Bonne année ! to:

• a friend
• a family member
• a teacher
• a colleague
• a customer

If you want to sound more formal or complete, you might add something like:

• Je vous souhaite une bonne année. = I wish you a happy new year.

But the short form Bonne année ! is perfectly normal in both informal and many formal situations.