Xmodem is explicitly a file transfer protocol (of great antiquity); the "terminal program" that initially implemented it (for CP/M!) was called just "MODEM." YMODEM and ZMODEM were later versions of the protocol.
These were all widely implemented by "terminal programs" from many vendors in the "Ethernet costs at least $1000/node and Internet isn't available to the common man" era (ie prior to the mid-1990s.) There was also Kermit, designed to (additionally) address problems with the transparency of long-distance serial connections... There is some (perhaps interesting) history here: GitHub - WestfW/TOPS20-MODEM: The TOPS20 implementation of X/Y/ZModem, as used at SIMTEL-20.
I would like to have the Arduino transfer the received file\image via its serial connection to appear in a folder on the PC.
XYZModem and Kermit are all reasonable candidates for transferring files from Arduino to PC, protocol-wise. The (A) problem is that the PC-side software that implements these protocols tends to be designed to be the "command side" of the connection - you run a "terminal program with XMODEM" support on your PC, use it to connect to some other device, start up XMODEM on that device, pop into the terminal program's command mode, and start the transfer from the PC side.
For the OP's Application, you want some sort of "server program" on your PC that runs in the background and listens for file transfer requests. Preferably without interfering with other functions of the serial port. I don't know whether such an application exists 
The Arduino-side code to send a file would be relatively trivial. The BASIC code to do it was about 30 lines... (but you'd probably want at least "YMODEM", which transmits filenames as well as the file data.)