Yes there is syntax problem, try your sed command as this:
sed -i "s/a'/à/g" "$1"
sed -i "s/e'/è/g" "$1"
sed -i "s/i'/ì/g" "$1"
sed -i "s/o'/ò/g" "$1"
sed -i "s/u'/ù/g" "$1"
Problem was that you were using nested single quote (quote inside code).