Mail regarding someone accessing my account

Apple will always address you by your name or the name they have on file for you, not Dear Customer, Dear Client or by using your e-mail address.  The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple emails won't have poor grammar/misspellings. Apple e-mails will never contain an attachment. Apple will never request personal information by email such as Social Security numbers, your Mother’s maiden name or full credit card numbers . 

The only exception to the above I have noticed is if you order something from the Apple Store (apple.com), your receipt will be addressed to Dear Apple Customer. That is a receipt for a purchase you initiated.

Hard to say for sure based on the info you gave now. But it seems likly it is a phishing email.

Does it use your name, not just your email adress?

If it does not its fake for sure.

Also check if it is from an apple email address.

Take a look at these articles

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

Identify legitimate emails from the App Store or iTunes Store - Apple Support

You can report it by forwarding it to reportphishing@apple.com.

Hope this helps!

You are welcome.