Elle était très excitée.

English Translation

She was very excited.

excité means something more explicit, right? hâte feels more right here?

The translation is correct, but, as you pointed out, it can have a sexual connotation (as it does in English, although in French that use might be more prevalent than in English).
However, to use “hâte”, you would need to change a bit the sentence to be “Elle avait hâte (de qqch)”, and it might not be the most direct translation, as it means “to look forward to”.

Hugo from Inner French suggests: avoir de hâte de as well: https://www.youtube.com/watch?v=1hxeVSy8wlM (and to avoid excitée)

Gemini suggests:

"If you mean she was happy, eager, or looking forward to something, you should use these alternatives instead:

1. Elle était impatiente (She was eager/couldn’t wait)

This is the best translation for “excited” regarding a future event (a trip, a concert, a date).

Meaning: She looked forward to it eagerly.

2. Elle était ravie (She was delighted/thrilled)

Use this if she was happy about good news.

Meaning: She was very happy.

3. Elle était enthousiaste (She was enthusiastic)

Use this if she was excited about an idea, a project, or a proposal.

4. Elle avait hâte (She was eager)

Use this with a verb.

"Elle avait hâte d’y aller." (She was excited to go there.)"

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