I had the same problem and specifications of Filemaker Pro 11 (and previous) explain that is not able to fallback a font.
This looks like it means that for whatever reason the euro sign is not being used as an Unicode character but an ASCII one. Change the font to Arial or Times Roman or any of the fonts included with the Mac OS and the euro sign will appear when saving as PDF.
Really, it is a matter of trying every font. For example, Garamond Premier Pro shows the euro sign in PDF but Myriad Pro doesn't.