Most faxes from the past decade are CCITT Group 3 or 4, containing image/g3fax or image/g4fax data which is encapsulated, or rather modulated, in one of V.27, V.29, V.17, V.34, or V.34bis.
Note that the fax transmission is not so-much a transmission, as a 2-way communication. Thus, you cannot simply play this audio back into a fax machine and expect it to work. However, luckily, the fax image data transmission itself is uninterrupted, so it is possible to filter out the unnecessary data.
What you will need to do is demodulate the content to retrieve the binary fax session and to filter out and extract the image/g3fax or image/g4fax data.
The late Tony Fischer wrote a software fax demodulator for V.34. It only works on Irix, so you'll need to port it. There was a Linux port at some time, but I couldn't find any valid links. http://www-users.cs.york.ac.uk/~fisher/software/modem/current/
There is also the Linmodem project.
Between these resources and some C programming, you should be able to extract the faxes... this isn't for the faint of heart, but possible, if the data is that important to you.