Hello Pierre,
Internally at
edx.org we use a 3rd party bulk mailing service provider just because of the scale of
edx.org (we just hit 5 million registered users).
I'm not aware of an internal tools in Open edX to do this. If you are interested in taking this on, I'd suggest you make this a Django management command in the LMS. It probably wouldn't be too hard (maybe 1 week's worth of work). I'd suggest making the an email template (the out frame of the email) via the Django Admin website and then - on a per email blast - inject in the body content.
You'd probably want a optional parameter on your management command to be able to send a single test email to one email address.
Best,
Chris