Might be a bit ugly, but echo -e should do it:
echo -en "$(curl $URL)"
-e interprets escapes, -n suppresses the newline echo would normally add.
Note: The \u escape works in the bash builtin echo, but not /usr/bin/echo.
As pointed out in the comments, this is bash 4.2+, and 4.2.x have a bug handling 0x00ff/17 values (0x80-0xff).