First of all, depending on what actions you would like to take with those leads, remember that some form of consent is needed in order to send them an email, etc. Grabbing everyone who liked your fan page and sending them an email without consent wouldn’t be a good idea, that’s why the Lead Forms are in place in both below solutions.
For Marketing Cloud integration, you would need to get Advertising Studio enabled in your account to be able to use Lead Capture in Advertising Studio.
To connect your Facebook advertising leads with Marketing Cloud Data Extensions in real time, use Advertising Studio’s Lead Capture feature.
Before you use this feature, you must:
-Enable data extensions in your Marketing Cloud account
-Create a Facebook lead advertising form
-Have admin level permissions on the Facebook page associated with the lead advertising form
Source: https://help.salesforce.com/articleView?id=mc_ads_lead_capture.htm&type=5&sfdcIFrameOrigin=null
For Sales Cloud-only integration, you can use Salesforce Lead Capture
Automate the flow of customer information directly from Facebook into Sales Cloud for sales teams to manage lead pipeline directly. Leads appears automatically in real time, using a secure connection to Facebook.
Source: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000DrzmfUAB