Thank you for your post.
FileMaker Server was certified to run with Java 8 Update 31, and it was bundled into the product installation. This ensure the minimum version of Java is installed onto machines. Users can download and install more recent versions of Java.
Thank you for the more critical information about FileMaker Server being susceptible to Logjam Attack. I have forwarded this information to our Development and Testing teams for review. When I receive any feedback, I will let you know.
You're shipping a Java version that expired in April/May this year;
Java™ SE Development Kit 8, Update 31 Release Notes
If you ship Java, updating your bundle is something you should do on a regular basis, including any internal certification. I understand that this might take a while, but a lag of six months or more is a bit irresponsible.