Existentialism is mostly incompatible with Rationalism
Existentialism goes a little deeper than believing people make irrational choices. It holds rather more broadly that the world itself is an irrational place, and the only meaning in the world is that which we give it. Rationalism says that people are primarily rational and derive meaning from reason, while Existentialism says that meaning is personal.
Example: A grandfather dies. One grandson says he dies because his heart stopped beating. One says he dies because God willed it. One says he died because a lifetime of smoking and eating unhealthily. One says he died because he failed to pray to the great Cthulu for mercy.
Clearly, for each grandson the death carries a drastically different meaning. Existentialists say that each grandson is just applying his own meaning to a random, absurd act of the world. In fact, some Existentialists say that to try to constrict meaning to some set of rational rules the world must follow prevents finding meaning in freedom.
This is pretty much in direct contradiction to Rationalism, which would claim that most people should rationally derive the true meaning of an event given the undeniably true structure that defines the world. Basically, there was a reason of death that fits into a larger structure, and most people should be able to act understanding this structure.
Existentialism does not deny all laws
Just because Existentialism denies that there is a grander meaning to the whole world, it doesn't deny that some things and laws are universal and true. This is Facticity, and this is where it starts to get weird.
Existentialists acknolwedge that some things are true, and that truths carry limitations. If you do not have legs, that is pretty much an undeniable fact. And the limitation of not being able to walk on the beach is a pretty strict one. Nobody denies that. What they do contest is that facticity doesn't have to follow reason, or remain constant. With enough science, or prayer, you may one day in the future grow legs and walk again. The facticity has changed. The important thing is that there is not necessarily a pattern to it. The value one places on facticity is purely free.
You do not have legs: this is a fact.
What this means: is entirely up to you.