Have you used any FTP client to access files on FTP servers? If yes, then how will you like to connect with the FTP without the use of any FTP client, just like you open any hard disk partition on your computer from your My Computer Windows Explorer. Yes it is very possible with a lightweight windows tool called NetDrive.
With NetDrive you can access any FTP server or WebDAV server from your My computer on your Window PC. All you need to do is to install this tool, fill the credentials once, select a drive letter and connect to the server.
Once you fill up the correct credentials, it will connect it to the server, automatically add a drive to your Windows explorer. You can select to launch NetDrive with Windows startup and automatically mount the drive when the PC starts up.
After you are done with connecting, just open the My Computer in Windows PC and there you find the FTP or WebADV drive like any other hard disk drive partition and you can open, access and edit file the way you do with your hard disk files.
I tested it on some FTP server and tested the functionality. You can also download and try out NetDrive as its free for personal use. Please note that if you intent to use it commercially, you need to purchase a license for it.