Marie souhaite une bonne année à Paul.

Souhaite is the 3rd person singular present tense form of the verb souhaiter.

So:

• je souhaite = I wish
• tu souhaites = you wish
• il/elle souhaite = he/she wishes

In Marie souhaite une bonne année à Paul, souhaite agrees with Marie, so it means Marie wishes...

French usually needs an article before a singular countable noun.

So année normally appears with an article such as:

• une année = a year
• l’année = the year

Here, une bonne année literally means a good year.

Even though English often says Happy New Year without an article, French grammar here treats it as the thing being wished: a good year.

In French, some adjectives come before the noun, and bon / bonne is one of the common ones.

So:

• une bonne année = a good year
• un bon livre = a good book

This is normal adjective placement. Not all French adjectives go before the noun, but bon / bonne does.

Because souhaiter often works like this:

souhaiter quelque chose à quelqu’un
= to wish something to someone

So in this sentence:

• une bonne année = the thing being wished
• à Paul = the person receiving the wish

That means:

• direct object: une bonne année
• indirect object: à Paul

English usually says Marie wishes Paul a happy new year, without to, but French uses à before the person.

Yes. That is also correct.

Both are possible:

• Marie souhaite une bonne année à Paul.
• Marie souhaite à Paul une bonne année.

The meaning is the same. French often allows both orders with this kind of verb.

Very often, putting à Paul earlier can slightly highlight the person receiving the wish.

Often yes, but not always exactly.

In this sentence, it works very similarly:

• souhaiter quelque chose à quelqu’un = to wish someone something

Examples:

• Je te souhaite bon courage. = I wish you good luck / strength.
• Nous vous souhaitons une bonne journée. = We wish you a good day.

But English sometimes uses wish in ways French does not copy directly. So it is best to learn common French patterns, not assume every English use of wish matches perfectly.

Because année is a feminine noun.

French adjectives usually agree with the noun they describe in gender and number.

• un bon livre = a good book
• une bonne année = a good year

So:

• masculine singular: bon
• feminine singular: bonne

Yes, absolutely. In real life, Bonne année ! is the very common greeting.

That is the short expression people say directly, just like Happy New Year!

The full sentence Marie souhaite une bonne année à Paul is a complete statement describing what Marie is doing.
But when speaking to someone, you would very often simply say:

• Bonne année !

It would usually become lui.

So:

• Marie souhaite une bonne année à Paul.
• Marie lui souhaite une bonne année.

Here, lui means to him.

If the recipient were plural, you would use leur:

• Marie leur souhaite une bonne année. = Marie wishes them a happy new year.

A simple pronunciation guide is:

ma-REE soo-ET uhn bon an-NAY ah POHL

A few helpful points:

• Marie sounds like ma-REE
• souhaite is roughly soo-ET
• une has a French vowel that does not exist exactly in English
• bonne année has a clear break between the two words, though it flows smoothly in speech
• Paul sounds like Pohl

A more IPA-style pronunciation is approximately:

/ma.ʁi su.ɛt yn bɔn‿a.ne a pɔl/

Yes. Souhaite is in the present tense.

So the sentence means that Marie is wishing Paul a happy new year, or wishes him a happy new year.

French present tense can often translate into English in more than one natural way, depending on context:

• Marie wishes Paul a happy new year.
• Marie is wishing Paul a happy new year.

Because the French expression is built differently.

French often says bonne année, which literally means good year, but it is the standard way to express Happy New Year.

So even though English includes new, French does not need to say nouvelle here in the usual greeting.

• Bonne année ! = Happy New Year!

This is a good example of why translations should be understood by meaning, not word-for-word.