Answer:
The correct phrase would be: "He and I want to attend the festival tomorrow"
Step-by-step explanation:
The pronouns "He" and "I" are personal pronouns that should be used as the subject of the sentence. On the other hand, the pronouns "Him" and "me" are those that are suffering the action of the verb of the phrase, they can not be used as subjects. In the sentence placed in the question, the pronouns should be the subject of the sentence, for this reason, "He" and "I" should be used.
The subject is one of the essential terms of prayer, usually responsible for carrying out the action of the verb.