The other answer has shown how to do this properly. But fundamentally the issue in your command is the lack of quoting, due to the way the shell expands variables:
rm -f $f
needs to become
rm -f "$f"
In fact, always quoting your variables is safe and generally a good idea.
However, this will not fix your code. Now filenames with spaces will work, but filenames with other valid characters (to wit, newlines) won’t. Try it:
touch foo$'\n'bar for f in $(find . -maxdepth 1 -name foo\*); do echo "rm -f $f"; done
Output:
rm -f ./foo rm -f bar
Clearly that won’t do. In fact, you mustn’t parse the output of find, for this reason. The only way of making this safe, apart from the solution via find -exec is to use the -print0 option:
find "$REP" -type f -name "$Filtre" -mtime +"$DelAvtPurge" -print0 \ | IFS= while read -r -d '' f; do rm -f "$f" done
Using -print0 instead of (implicit) -print causes find to delimit hits by the null character instead of newline. Correspondingly, IFS= read -r -d '' reads a null-character delimited input string, which we do in a loop using while (the -r option prevents read from interpreting backslashes as escape sequences).
