I doubt if an Arduino is the ideal solution for this.
It may just be possible, although I've never done anything like this, using say the ESP8266 with an SD card. Use an FTP client on the ESP8266 to fetch the file to the SD card (assuming your storage on the local network is accessible via FTP), rename the file on the SDcard, and stream the file (somehow, maybe using a Web method) to your SQL server. There may also be better ways of doing this.
Edit:
It may be, however, that an Arduino Yun (or similar Unix Hybrid) could be a possible platform for this and may have more possibilities for accessing your local file storage using SMB or similar.