I am not sure to understand that command. Why do you put -- before the %F?
Try this:
xfce4-terminal -e "parallel avconv -i '{}' -map 0:1 -c:a copy '{}.m4a' ::: %F"
Explanation: As I understand the %F is what Thunar replaces by the files, and parallel uses ::: for the input.
One example in the manpage is, precisely
parallel gzip {} ::: file1 file2
To add to Thunar custom action a command like the one from here
for i in *.mp4; do avconv -i "${i}" -map 0:1 -c:a copy "${i%.mp4}.aac"; done
first add that into an executable script, like
#! /bin/sh -e
for i in *.mp4; do avconv -i "${i}" -map 0:1 -c:a copy "${i%.mp4}.m4a"; done
Make it executable and save it.
In Thunar custom actions add a new entry with the command bash /path/to/the/script %F and the following conditions:

This needs separate custom actions for each file type (because it is limited to mp4 to m4a: make changes accordingly for flv to m4a, webm to ogg, avi to mp3 etc) but has the advantage that the output keeps the exact input name (file.mp4 becomes file.m4a), while with the first command does not (file.mp4 becomes file.mp4.m4a).