On Prem FTP Client cannot connect to S3 through AWS Direct Connect Link

The FTP client will not be able to connect directly to the VPC endpoint for the S3 bucket. You need to put an AWS Transfer Family FTP server in front of the S3 bucket and then connect to that https://docs.aws.amazon.com/transfer/latest/userguide/create-server-ftp.html

Note that plain, unencrypted FTP is supported for your use case (access over a Direct Connect link) that is one of very few use cases for which it is supported. Unless there is a good business reason for using FTP, it would be strongly advised to consider SFTP or FTPS https://repost.aws/knowledge-center/aws-sftp-endpoint-type

What's the VPC endpoint you mentioned - is it an Interface or Gateway endpoint? You won't be able to use a Gateway endpoint from on-prem. Your choices are Public VIF or Interface endpoint over Private or Transit VIF. To use an Interface endpoint you need network connectivity to it and also resolution of the DNS name for the service to be that endpoint. For on-prem that's achieved by using a Route 53 Resolver Inbound Endpoint to delegate resolution of the S3 service name.