Phishing mails are nothing new. Recently, some phishing mails have taken to use threats of blackmail by claiming they have sensitive information and/or have compromised the PC.
For the most part, mails like those are empty threats, designed to get users feeling insecure and worried about the potential info that may be in the possession of the mailer.
An easy way to calm users down is to perform a Google search using the exact text of the mail and the results of the search should be enough to show end users that this is a standard bulk scam mail being sent to likely thousands of random email addresses, making the threat less believable.
Sending out a notification to users about current scams being seen in inboxes, is always a good idea - that can help prevent users from clicking where they shouldn't and keep their wits about them.
If a threat or compromise turns out to be real, obviously lockdowns, AV cleaning and forensics needs to be performed in line with the best practises for intrusion cleanups.