You may use emoi to translate to be agitated or an excitement in the other hand emotion is more used to translate emotion or feeling

Please note that emoi use in french is more uncomon than emotion.

If we look at the definitions in a French dictionary aka monolingual dictionary, we learn that the word émoi is considered literary.

The Larousse Dictionary says this for émoi:

Littéraire

1. Trouble causé par la crainte, l’inquiétude ; effervescence : La ville est en émoi. [Worry or upset or being troubled [as in Je suis troublé] as caused by fear, disquiet, etc.]
2. Émotion vive causée par l’inquiétude, la douleur ou la joie, la sensualité, etc. : L’émoi du printemps. [strong feeling or emotion]

and this for émotion:

(de émouvoir, d’après l’ancien français motion, mouvement)

1. Trouble subit, agitation passagère causés par un sentiment vif de peur, de surprise, de joie, etc. : Parler avec émotion de quelqu’un. [the troubled state that is undergone, a passing disquiet caused by a strong feeling of fear etc.]
   Synonymes : émoi (littéraire) – exaltation – fièvre [exaltation and fever]
   [English for that: emotion, upset due to surprise, fear, etc.

2. Réaction affective transitoire d’assez grande intensité, habituellement provoquée par une stimulation venue de l’environnement.
   Synonymes :

commotion – ébranlement – saisissement – secousse

3. Sous l’Ancien Régime, révolte populaire non organisée et généralement de courte durée.
   Synonyme : fureur

The main reason I gave the French meanings is to show that émoi and émotion can basically be the same but one is literary and the other is not. You might not learn that with a bilingual dictionary. émoi is often found in newspapers and writing. It is also formal and less likely (but not unlikely) to be used in everyday conversation.

Also, for me, when émoi in a particular context means exaltation, that is what most differentiates it from émotion. Whereas where they both mean emotion, they have the same meaning.

In any event, with a context, one is just left to translate individual words and language doesn’t work like that in the real world, only the dictionary world. Please note: I did not translate every single nuanced meaning here.
Larousse