All email addresses contain an 'at' (i.e. @) symbol. Test that necessary condition:
email.includes('@')
Or, if you need to support IE/older browsers:
email.indexOf("@"'@') > 0
Don't bother with anything more complicated. Even if you could perfectly determine whether an email is RFC-syntactically valid, that wouldn't tell you whether it belongs to the person who supplied it. That's what really matters.
To test that, send a validation message.