You can find and download a special script from Adobe that allows users to import old FreeHand drawings (like .fh11) directly to Adobe Illustrator and save them as .ai drawings, essentially achieving fh11 to ai conversion. Unfortunately, this option seems to be only working for CS4/CS5 versions of Illustrator and of course if you do not have access to Illustrator, you won't be able to perform fh11 conversion of any kind.
Open FH11 file Open AI file
A powerful vector graphics editor from Adobe
Mac version of Adobe's vector graphics editor