I would say

Profite bien !

From profiter.

Or even simpler

Profite !

It’s not necessarily associated with fun and fits perfectly in your exemple “Enjoy the wedding !”.

The “enjoy“s in French come in all flavours, far from being confined to a single translation.

1. To express the idea of “enjoy the concert / wedding day!”, I’d probably say:

Donnez-vous en à cœur joie ! — « s’en donner à cœur joie »

… to tell them to make the most of the joyous occasion.

2. « S’amuser » leans towards having mindless fun. For instance:

Ça te dirait de me laisser me joindre à votre groupe ? Vous avez l’air de vous amuser.

3. When it comes to culinary delights, « se régaler (de) » comes in handy:

Je t’ai préparé une tarte aux fruits de saison. Régale-toi bien !

4. Speaking of culinary delights, you can use « déguster », but not « régaler », in the following:

Comment veux-tu qu’on déguste un bon vin dans un resto ultra bruyant !?

5. I’d never use « jouir » to say “enjoy the concert!”; « jouir » is more about enjoying something like a privilege that you are entitled to, immense popularity, or good health, as in:

Elle jouit d‘un rang distingué, mais elle ne s’en vante pas.

6. As for the music context, « aimer » fits the bill to express the idea of “enjoy doing”:

J’aime écouter la musique.

7. As an exclamatory “Enjoy something!”:

« Bon voyage ! » « Bon appétit ! » « Bon film ! »

8. « Profiter » meshes well with the English expression “enjoy everything something has to offer”:

Une semaine ne suffit pas pour profiter de tout ce que le Canada a à (vous) offrir.

9. I’d use only « savourer » in the following instance:

Savourez pleinement la vie !

There isn’t a single translation. French tends to use more specific words that denote a specific kind of pleasure.

“Amuse-toi bien” is one of the contexts where amuser can mean happiness-fun and not just haha-fun. You can say this about a concert or a wedding. After the concert, “j’ai aimé” (or “j’ai adoré” or another near-synonym) is the natural way to convey this sentiment, whereas “je me suis amusé” says that there was at least a bit of haha-fun. “Bon X” works better for some X than others, for example “bon voyage” and “bon week-end” are extremely common whereas “bon concert” is ok but sounds slightly weird.

Jouir doesn’t work, even if you don’t care about the possible sexual meaning. In the sense of “enjoy”, jouir is either extremely old-fashioned, or usable in informal contexts that are very hard to pinpoint, often with no complement to mean “I’m happy”. It’s rather hard to gauge so I recommend that non-natives avoid it.

As Alone-zee notes, for food (and drink), se régaler works, both as a wish and as a declaration: “Régale-toi !”, “Je me suis régalé.”.

For the sake of completeness and fun, may I bring to your attention the delightful “enjailler” (of Ivorian origin it seems). “On s’est bien enjaillé.”