If a note is added by a third party (reply to a ticket forward), as of now Freshservice would not have a default email notification which would be sent to the Agent. Instead, you would have to configure a Workflow Automator(Admin-->Workflow Automator) to send out the Email Notifications in such cases.
1. When these actions are performed by Requester
2. When these events occurred: Note added is Private
1. On tickets with these properties: Leave Blank
Set status as Open
1. Set Status as 'Open' or any custom status (optional)
2. Send email to Assigned Agent
3. Type in your Content of the email