Unless Filemaker Pro v6 was written in Universal Binary, and judging by your post it was not, FMPV6 will not run on Lion or Mountain Lion.
The problem is that FMPV6 was written for the PPC processor and all support for that processor was dropped when Apple released OS X 10.7
To see how a particular app is coded, select the app, Right Click and choose Get Info. (or select the app and Control + Click). Look at the line that says Kind. If it says Application, Universal Binary, UB or Intel, it should run.
If it says PPC, forget it.