Le Pprince

No need to capitalize "prince" here

Il prendmonte sur le trône après de recevoiravoir reçu la couronne.

"prendre le trône" isn't said; the most usual expression is "monter sur le trône"
après avoir fait (past infinitive for an accomplished action)

Duranst cette célébrintronisation, tous deviennent ses amis.

The ceremony during which a king sits on his future throne is called "une intronisation", which is part of a greater process called "un couronnement" (a crowning)

[Ils ne voient pas que leur avenir. ?]

Given the context, I rather think you meant "they ONLY think about their future"
ne/que = only (if you add a "pas" you're making a double negative with the opposite meaning!)

Le roi reçOn fait au roit le meilleurplus insigne honneur quand il sort sur le balcon et il entend les cris de la foule.

The usual expression is "faire honneur à quelqu'un". "Recevoir les honneurs" do exist, but it rather means "being congratulated" instead of truly being honored, which is "recevoir un honneur"
insigne honneur = distinct honor (the adjective very often goes with "honor")
There are several people screaming, so "cri" would be pluralized

Toust le gentsmonde se rappelle quand le roi a crié : « Vvenez-, (vous,) tous qui veoulent a la célébration!z assister à l'intronisation/la cérémonie ! »

everybody = tout le monde (no one says "tous les gens",it feels clumsy)
There is no uppercase after a colon or semicolon
"qui" repeats "vous" here, so it would imply a verb with a 2PS agreement => vous voulez (a verb was also missing afterwards)

». Tous ceux qui veoulaient, pourrvaist assister à la fêtcérémonie, mais ils doivevaient apporter un cadeau.

Literally "all those who wanted" => tous ceux qui voulaient
Past tenses => voulaient, pouvaient, devaient