The bad thing is you're going to have a lot of redundant emails, and if you try sending out a newsletter about the revival, you may have people marking the email as junk/spam. Which in turn is bad for the IP address you're on, unless you're using a third-party system to send the emails (of which, many providers want you to use a clean list that will have less than 5-10% bounced emails).
I think it may be best to start fresh, but do indeed go for sending out a single email to those that may be interested. Give them plenty of details in the email, and most of all: give them a reason why they should come back.
A lot of forums have loyalists that really only left once the inevitable happened to the site; those are good people to keep in touch with, if you can. They may be good assets for your new forum venture.
For one, forums are not popular anymore and they are on their way out.
I disagree that forums are on their way out (overall), but I do agree to an extent. Social media is still and will continue to be strong. The problem with traditional forums is that they try to stick to the old formula, rather than going just that way: a social media site. If forum software would adapt the way that social media has, many more forum-focused sites could very well thrive.
Another problem with a standard forum is that they are generally about standard topics that have been done over and over again. You will notice, though, that forums out there that
provide value to its users are still kicking and continuing to grow. A lot of forum admins don't know how to provide that value though.