Accessing Elastic Beanstalk Application files from FTP Client

Generally, it is not a best practice to directly modify the already deployed files, this is because when you make an environment update either from console or EB CLI all the files will be replaced again from the new application version source bundle downloaded from S3. In order to make persistent changes, you would need to deploy a new version to the environment[1][2]. The easiest way should be using eb cli which will allow you to deploy from your local machine's directory. Regarding your question, the permission denied error is either due to access limitation for the FTP user to write to the files under /var/app/current or the FTP configuration does not allow file modification. You can login into the instance and switch as ftp user and check if the user can make changes to the files as expected.

[1] https://docs.aws.amazon.com/elasticbeanstalk/latest/dg/using-features.deploy-existing-version.html
[2] https://docs.aws.amazon.com/elasticbeanstalk/latest/dg/eb3-deploy.html