I am not familiar with xsel so I have no idea what causes your problem.
But independent of that in general you should not run more external commands than necessary so the simple solution to your problem is:
#!/bin/bash
xsel="$(xsel)"
firefox 'https://en.wiktionary.org/wiki/'"${xsel}"'#French'
echo "${xsel}$(date +": %Y-%m-%d (%a)")" >> fr/word-list.txt