To begin your e-mail, you can use:

Monsieur/Madame le/la Directeur/Ministre/…,

Chère Madame X (or Cher Monsieur X)

Bonjour Madame X (or Monsieur X)

Monsieur, Madame X

Cher/Chère X,

Bonjour X,

Bonjour,

Salut X,

Salut,

They are roughly from the more formal to the less formal.
Note that some women prefer “Madame la Ministre”
while other like “Madame le Ministre”.
You probably do not want to get involved in such a fight
so I’d suggest you avoid this solution.

“Dear X” can be directly replaced by “Cher X”. Note that you have to write “Chère X” instead if you know X to be a woman.

“I hope you are well” can also be safely replaced by its almost-literal translation: “J’espère que vous allez bien.” Other equivalent formulations can be used but this one is very common.