You could start with this:
#!/bin/bash
shopt -s extglob || {
echo "Unable to enable exglob."
exit 1
}
TARGETEXT='.avi'
TARGETPREFIX='/path/to/somewhere/' ## Make sure it ends with /.
while IFS= read -r FILE; do
BASE=${FILE##*/}
NOEXT=${BASE%.*}
TARGETFILEPATH=${TARGETPREFIX}${NOEXT}${TARGETEXT}
echo ffmpeg -i "$FILE" "$TARGETFILEPATH" ## Remove echo if it's already correct.
done < <(exec find -type f -name '*.mov') ## You could also use -iname '*.sh' instead.
Of course you could use a custom directory to search for the files:
find /path/to/directory -type f -name '*.mov'