The version in Aur is outdated. I downloaded the current version from Floorp’s website but I couldn’t install it.
Here is the content of tarbz2:
application.ini
browser
defaults
dependentlibs.list
floorp
floorp-bin
fonts
glxtest
gmp-clearkey
icons
libfreeblpriv3.so
libipcclientcerts.so
liblgpllibs.so
libmozavcodec.so
libmozavutil.so
libmozgtk.so
libmozsandbox.so
libmozsqlite3.so
libmozwayland.so
libnspr4.so
libnss3.so
libnssckbi.so
libnssutil3.so
libplc4.so
libplds4.so
libsmime3.so
libsoftokn3.so
libssl3.so
libxul.so
omni.ja
pingsender
platform.ini
plugin-container
precomplete
removed-files
updater
updater.ini
update-settings.ini
vaapitest
This is a good chance to do some learning! Try building & installing from source. The AUR is just a bunch of scripts to do exactly that.
Once you can do that, try updating the PKGBUILD yourself.
Edit: the repo on github (or wherever the project is maintained) will have installation instructions. It will involve terminal commands, and you will likely need to have other stuff (dependencies) installed first.