You do not need a fax modem - that would rather defeat the object of the exercise. You do need an isolation device which will pass audio signals unchanged from the 'phone exchange to your Indy and vice versa, and protect both exchange and Indy from (e.g.) lightning strikes on the 'phone line or disastrous power supply failures in the Indy.
In the USA such an isolation device is called a Data Access Arrangement (DAA), and is available at low cost from (e.g.) Cermetek.
In the UK things are a little more complicated. There is a Post Office approved device called a Line Terminating Unit (LTU), made by GEC Plessey around 1980 for the Viewdata trials, which does the job. A basic LTU consists of little more than an isolating transformer (price ~£2.50 from RS or Farnell) and a relay (about the same price, from the same suppliers). In the UK an LTU must be approved by BABT before you connect it to a 'phone line - you'll need one of these.
If you want to see a circuit for a (rather high quality - some might say over-engineered) LTU, there's a scanned-in image of one here. Sorry about the poor image quality. This one was designed for a student project, to be used on an exchange line simulator, so it doesn't have a you-know-what.