Not a quite a falx but I've been doing
medieval reenactment for many years (professionally)— I ride
steeds and have jousted (in full armor).

I have used large double edged swords (european style) from horse
back and I can say that without stirrups they are
not easy to handle. A falx would be even more difficult.

You might be able to scare someone with it from
horseback but to use this weapon, in the thick of battle
(with a shield no less) would be folly!

Now, it could be these guys dismount and then use them.
That is a possibility.