I have a bot that I am building with the help of the Microsoft Bot Framework. I can see that session.message.user.id gives us the user id and session.message.user.name give
The only way is to specifically ask the user for their email and then for example save it in user data in the bot.
Facebook (luckily) doesn't give out users' emails to bots. A normal Facebook app, on the other hand, might get it.
List of available fields: https://developers.facebook.com/docs/messenger-platform/identity/user-profile#fields