Ancestry.com and Family Tree Maker Software
Ancestry.com has changed their software and no longer uses the AFT format. While their new software does have an Import utility and this Import utility is supposed to import AFT files, many users have reported a "file not recognized" error when using this option. First, make sure that you have the latest updates of the software just in case Ancestry.com has fixed this issue. If not, it's time to get creative.
I've searched the Ancestry.com support site and many forums and was surprised that no real solution has been offered. However, I was also pleasantly surprised to see that Ancestry.com does have a link to the old software (buried deep within their pages).
Download the Old Family Tree Maker Software
What I would do first is go to Ancestry.com and download the old software. The link to their old version of Family Tree Maker is posted here. From there, you should be able to work with your files as before. You may be able to then export the files into one of the other more compatible formats using the Export utility.
Try Ancestral Quest Software
If for some reason the link to the old version of Family Tree Maker doesn't work, then you might want to try Ancestral Quest Software. This option might cost you a few bucks but I think it will work. According to the Frequently Asked Questions at Ancestral Quest, AFT files are identical to Ancestral Quest's .AQ files. This means that if you had a copy of Ancestral Quest, you could open your AFT files and work with them. You could also potentially export them to a more compatible format. Ancestral Quest offers a free trial of the software but it restricts the number of entries to 40 people. The full version costs about $30. You can check it out at http://www.ancquest.com/.