There are a few options you could try, but I have never tried to transcode blu-ray myself
Firstly there is Arista Transcoder (available from the software centre)
Kdenlive, Kino, Openshot, Avidemux, and Pitivi are all intuitive and powerful multi-track video editors, including some of the most recent video technologies.
K3b is a CD and DVD authoring application for the KDE desktop environment for Unix-like computer operating systems. (works great in Unity) It provides a graphical user interface to perform most CD/DVD burning tasks like creating an Audio CD from a set of audio files or copying a CD/DVD, as well as more advanced tasks such as burning eMoviX CD/DVDs. It can also perform direct disc-to-disc copies.
sudo apt-get install k3b k3b-data libk3b6
Also available from the Software centre
HandBrake is an open-source program designed to convert MPEG video (including DVD-Video) into an MPEG-4 video file in MPEG-4 Part 14 (.mp4) or Matroska (.mkv) containers.
sudo add-apt-repository ppa:stebbins/handbrake-snapshots
sudo apt-get update
sudo apt-get install handbrake-gtk handbrake-cli