Vendredi, je souhaite un bon week-end à Paul.

French often uses a weekday without a preposition to mean on that day.

So Vendredi, je souhaite un bon week-end à Paul means On Friday, I wish Paul a good weekend.

This is normal in French:

• Lundi, je travaille. = On Monday, I work.
• Mardi, il pleut. = On Tuesday, it’s raining.

English usually needs on, but French often does not.

By itself, vendredi usually refers to a specific Friday, depending on the context: Friday / on Friday.

If you want the habitual meaning every Friday / on Fridays, French usually says:

• Le vendredi, je souhaite un bon week-end à Paul.

So:

• Vendredi = on Friday / this Friday / Friday in context
• Le vendredi = on Fridays / every Friday

Yes. In French, days of the week are normally lowercase:

• lundi
• mardi
• vendredi

Here Vendredi is capitalized only because it is at the beginning of the sentence. If it appeared in the middle, it would normally be:

• Je souhaite un bon week-end à Paul vendredi.

The comma separates the time expression from the rest of the sentence.

French often uses a comma when a short time phrase is placed at the beginning for emphasis or clarity:

• Vendredi, je souhaite un bon week-end à Paul.

Without the comma, the sentence would still be understandable:

• Vendredi je souhaite un bon week-end à Paul.

But the comma makes the opening time phrase feel more clearly set off, a bit like On Friday, ... in English.

Souhaiter means to wish.

It is the normal verb used when you express a polite good wish to someone:

• souhaiter une bonne journée = to wish someone a good day
• souhaiter bon courage = to wish someone strength / good luck
• souhaiter un bon week-end = to wish someone a good weekend

So je souhaite un bon week-end à Paul is a very natural way to say that you are wishing Paul a good weekend.

Because Paul is the person receiving the wish.

The pattern is:

souhaiter quelque chose à quelqu’un
= to wish something to someone
or more natural English: to wish someone something

In this sentence:

• un bon week-end = the thing being wished
• à Paul = the person receiving it

So French says:

• Je souhaite un bon week-end à Paul.

Where English says:

• I wish Paul a good weekend.

Yes. You would usually use lui:

• Je lui souhaite un bon week-end. = I wish him a good weekend.

Here, lui replaces à Paul because it is an indirect object.

So:

• à Paul → lui
• à Marie → lui
• à mes amis → leur

Examples:

• Je lui souhaite une bonne soirée.
• Je leur souhaite de bonnes vacances.

Yes. That word order is also correct.

You can say:

• Je souhaite un bon week-end à Paul.
• Je souhaite à Paul un bon week-end.

Both are grammatical. The version in your sentence is very natural and common.

Very roughly:

• Je souhaite un bon week-end à Paul puts the wish first.
• Je souhaite à Paul un bon week-end puts Paul a little earlier.

In everyday French, both are fine.

After the verb souhaiter, French normally uses an article:

• Je souhaite un bon week-end à Paul.
• Je vous souhaite une bonne journée.

But when the expression is used by itself as a greeting, French often drops the article:

• Bon week-end !
• Bonne journée !
• Bonne soirée !

So:

• after souhaiter → usually un / une
• as a standalone greeting → often no article

Because week-end is a masculine noun in French.

So the adjective must agree with it:

• un bon week-end
• not une bonne week-end

Compare:

• un bon week-end because week-end is masculine
• une bonne journée because journée is feminine

Yes. Week-end is very commonly used in French, even though it originally comes from English.

Standard French usually writes it:

• week-end

It is treated like a normal masculine French noun:

• un week-end
• le week-end
• bon week-end

So in your sentence, un bon week-end is completely normal modern French.