Three questions need to be answered to determine this:
- Is there a verifiable paternal line paper trail from Franz Joseph directly down to you?
- Has another male descendant who also has a verifiable unbroken paternal line of descent from Franz Joseph taken a Y DNA test?
- Do your Y DNA results closely match that of the other descendant?
If you can answer all three questions with a yes, then it is very possible to determine whether or not you descend from Franz Joseph.