I too would suggest Xpadder, you can use it to manually map controls to your joystick. I've tried it before to map a DualShock 3 controller and use it to play some multi-platform games, it worked quite well. It didn't have much lag and even if it did you wouldn't notice it.
But as a console and PC gamer, I must say the keyboard + mouse combination beats gamepads at shooters. Freelancer is a shooter.
Autohotkeys or perhaps Joykeys but joykeys is really need for ELite Dangerous anyways so i suppose it cant be that difficult to set it up for freelancer since its much less complicated controls.