If that truly is just a cable adapter, with no electronics hidden underneath that black overmolding, you're not going to be able to use it to connect to the analog telephone network.
USB uses its four wires for power, ground, and a differential signaling pair, all operating at 5 V DC.
POTS uses its four wires as two separate phone lines, with voltages up to 48 VDC. There's phantom power riding on those lines, and the audio signal is modulated on top of that voltage.
This vast difference between computer data signaling and analog phone signaling is the very reason we have analog telephone modems: they convert the signaling scheme from one format to the other, and vice versa.
If you use one of those adapters to plug a live analog telephone line into your computer, you're likely going to blow up the USB port.
The only reason those adapters exist is so you can transport USB over cheap wiring, especially existing wiring. They won't be any good for high-speed USB with most phone cable, and won't be good for much distance besides.
There are commercially-available USB analog telephone modems, compatible with Linux and OS X at least. You just plug them into the USB port and they appear as
/dev/ttyACM0 on Linux, meaning the OS sees them as USB-to-serial adapters. You configure them for PPP the same as you would any old-school RS-232 serial port, like
/dev/ttyS0 on Linux.