Good question.
I watch this project a bit from aside thinking it will be good for my chiidren.
I tried the Appimage now.
Appimage is good as it theoretically can run on all desktop Linux systems.
Unfortunately it fail here on Mageia 8 about the parts database, three error dialogues at start, then at every try at the parts side panel.
From my experience, Flatpak tend to be more successful for similar programs, so that may be a tip to developer.
One of our packagers tried to compile 0.9.6 for Mageia, failed at the database step, and bug for help is not answered yet: Building on Mageia Linux · Issue #3796 · fritzing/fritzing-app · GitHub
To get this marvellous piece to more users, some compiling help (and updated repo) and/or better Appimage (or Flatpak) compatibility is needed.
I payed another 8EUR today and writhe this to help push a bit 
Edit: I reported the AppImage problem at Provide Fritzing AppImage for Linux · Issue #3302 · fritzing/fritzing-app · GitHub /Edit
Edit2: I found a Flatpak of 0.9.6 at Flathub—An app store and build service for Linux seem to run nice: i could make new design and save, and open old 0.9.4 design, close and open app again, and it remembered last design, printed. Maybe this is not an official release? Should be, and updated More details at Install 0.9.6 on Linux - #7 by microMerlin /Edit2
/Morgan