This is a common problem of Linux with the 'winModems' like yours. I had to deal with it when I had dial-up internet too.
I suggest you go the manufacturers website and search for Linux drivers for your device, if they do have some Linux drivers follow the instructions to install them. (Don't expect a flawlessly installation though, you may be ready to install additional dependencies). If they don't have Linux drivers search them in Google, I remember there is page where they have many of them (think that someone had the problem before you).
In any case never expect Linux to automatically recognize your winModem (I was told however that the external modems work quite good), in my case I could succesfully use under Linux my Intel 536EP modem.
Notebook: Samsung NP355 V4C
AMD A6 VISION 4400M APU @ 2.7GHz, 4GB DDR3,
1TB Toshiba HDD, TSSTcorp DVD-RW.
Windows 7 Professional, Fedora 22 x86_64