Note: I'm not sure if this is true since there is a wine [afmdirs] section in the wine config. Wine still had troubles with (at least) some of the files.
Converting Type1 fonts to Truetype fonts was easy and Framemaker actually has a hidden feature to find out which fonts are missing. When you load your FrameMaker document and you have missing fonts, it wants to reformat your file. After you allow that, just look at the available fonts, suddenly you have a few extra ones in the list that have been disabled. These are the fonts FrameMaker requires and couldn't find.
Write down the names as they appear in the list, quit the document without saving (!), then go look for the Type1 fonts that match the name. The easiest way is to use grep on the filenames. Look for the .pfb, .pfa or .afm files.
Open them in fontforge (http://fontforge.sourceforge.net/), if necessary change the Family Name to what you wrote down and safe it as a Truetype font. If you do that for all the files involved until FrameMaker does no longer complain, you're ready to use FrameMaker :)
You can also use strings on the FrameMaker (.fm) files and look at the near end to find the names of the used fonts. But it wasn't always that clear to me.