Facebook does not advertise a telephone number for their customer service department. The best way to contact Facebook Customer Service is via the Facebook Help Center. As the How to Contact Facebook page states, "Unfortunately, there is no way to directly contact Facebook - you can't call, text, email, or otherwise speak to an employee or affiliate of Facebook. You can, however, use Facebook's Help Center to diagnose and report a problem with your account."
The Facebook Business forum includes a post called "How do I contact Facebook Customer Service?" that emphatically states (I'm adding the emphasis): "NOTE ON PHONE SUPPORT: We do not post a phone number for Facebook support. If you see a phone number for Facebook support, it is a scam." That post also provides links to Facebook Help on Keeping Your Account Secure and Avoid Spam and Scams. The Facebook Support Inbox is an appropriate place to contact Facebook support. The Facebook Safety Center also provides links to resources linked to using Facebook safely that includes information on hacked accounts (the best way to report to Facebook that you think your account has been hacked is to go to https://www.facebook.com/hacked).
The reason I am writing about this is because I'm aware of someone's Facebook account being hacked earlier this month and the approaches to dealing with that hacked Facebook account led to far more serious consequences than the hacked Facebook account by itself presented. It had appeared that a friend had sent a personal message on Facebook to see her video (it was a generic message and turned out to have been sent with nefarious purposes by someone who had hacked this person's Facebook account). When the video was clicked on, the recipient's Facebook account was also compromised. When that account started sending out similar suspicious personal messages to friends on Facebook, one of the recipients rightly observed that this indicated a hacked Facebook account. At the point of awareness of this hacked Facebook account, the best move would have been to report this to Facebook via https://www.facebook.com/hacked.
Unfortunately, the owner of this hacked Facebook account panicked when the alert friend warned of the account hacking. The owner of that hacked account searched on Google for "Facebook customer service 1-800 telephone number" and clicked on one of the links returned on the first results page. This linked-to page listed a 1-800 number allegedly for Facebook customer support and the Facebook account owner called that number. The people who answered the number sounded polite and helpful and quickly convinced the Facebook account owner to give access to the computer the account owner was using and then proceeded to install nastiness on that computer that resulted in the need for a complete wiping of the machine and re-installation of software. What started out as a hacked Facebook account with damage limited to what could be done with that account led to damage to the person's entire computer and the potential to have much more information lost if not handled quickly.
Here are current results of a Google search for "Facebook customer service 1-800 number":
I marked out the actual 1-800 numbers so that no one would accidentally use one of these numbers in attempt to contact Facebook Customer Support. It's also interesting that one of the results shown is for a customer called "CustomerSupportNumber" and I suspect that has nothing to do with actual Facebook Customer Service and all numbers listed there should be ignored (I'm surprised Facebook allows this account to exist and I intentionally do not link to it here). It is also worth noting that the first two results returned from the Google search appear to be fraudulent Facebook Customer Support pretenders because they do advertise a telephone number.
It seems easy to avoid problems like those discussed here, but in moments of panic and shock about a hacked account, it can also be easy to forget and fall into traps like those presented online by people alleging to be Facebook Customer Service and providing telephone numbers to contact them. In the case of Facebook, a telephone number advertised online should never be used. In more general cases, it's always best to find the contact number from the desired recipient's web site rather than from a Google search. In other words, the only telephone number for Faecbook Customer Service that could be trusted is one listed on the Facebook main page (look for https://www.facebook.com), but even that can lead to a mistake as the "CustomerSupportNumber" account on Facebook purports to provide Facebook telephone numbers, but I am guessing those are no better than the ones returned by the Google search.