The conclusion seems to be that conventions in French emails have become similar to those in English - despite French's reputation for being a more formal language than English.
At the more formal end, email opening staples are:
To whom it may concern / Dear Sir or Madam
Nowadays professional emails increasingly open with Bonjour / Bonsoir. Salut is for friends, not for professional emails.
I now regularly receive business emails from people that I've spoken to before, although not necessarily very much, which have no salutation at all but rather get straight down to it. I'm not a huge fan of this and, happily, it appears to be less common in France.
The vous/tu rules are simple - vouvoyer in emails if you would in real life, and likewise for the tutoiement
French has a few variations on the following very formal set phrase which are used at the end of letters and which can be used in official or very formal professional emails:
Veuillez agréer, Monsieur / Madame, l’assurance de mes sentiments les plus distingués
Yours sincerely / Yours faithfully
Merci de bien vouloir me répondre
Dans l'attente de votre réponse
Both mean something like "thank you in advance for your response"
A très vite
Thank you in advance
Waiting for your response
See you soon