If an entity existed such as Laplace's demon, that could know with precision the current state of the universe and - using the laws of physics - could tell you your future with certainty, would you then be able to change it?
As Jo Wehler pointed out, Quantum Mechanics made Laplace's demon impossible based on empirical evidence.
But if we ignore QM, your line of reasoning becomes very interesting: Isn't there a contradiction in the fact that if Laplace's demon could predict future events, she could also changes those events based on that knowledge so that the prediction is invalidated? In fact mathematician David Woplert used reasoning similar to yours to prove that Laplace's demon is impossible, no matter which laws of physics govern the universe. In a nutshell, he proved that no entity could ever fully predict a universe that it is part of. The only way Laplace's demon could pull this off is if they were outside of the universe (whatever outside of the uinverse means).
The idea is the following: Both observation and prediction are formalized in the concept of inference device, and he defines strong (i.e. universal) inference devices and self aware inference devices. Using what he calls inference complexity, he shows that there are limits to what such devices can predict, similar to the way the halting problem shows the limits of universal Turing machines.
His result is analogous in a way to Godel's "No theory can prove it's own consistency", in that he shows that no universe can completely predict itself (since physical inference devices are embedded within this universe).
Your question is not realistic because it builds on an impossible premiss:
Laplace could not know, but thanks to quantum mechanics we know today: It is not possible to determine the exact position and impulse of all particles, due to Heisenberg uncertainty relation.
This fact adds also a physical impossibility and complements the remark of user 259242 that the question is logical inconsistent.
I agree with Alexander King that this is an interesting question... if we ignore the fact that its suppositions have no current basis in physics. In that case, it is also a refined version of an ancient question.
It is, quite simply, the question of apparent natural determinism and apparent human freedom. One hardly knows where to begin! The need to reintroduce some sort of "quantum indeterminacy" into a picture of physical determinacy dates back to Epicurus and his use of the "swerve" to qualify the billiard-ball model of the pure atomists.
In my own view, the most refined philosophical attempt to reconcile physical, Newtonian "laws" with the representation of those "laws" and human "freedom" are Kant's, in which he structures a model based on two different modes of "causality," to put it over-simply.
As to your Laplace Demon, it is a historical oddity, emerging between the Newtonian world and the enlightened "freedom" of the French Revolution, actually shortly thereafter. Laplace did not, as Kant would do, attempt to account for the "outside" privilege of the observer.
Yet he was also a father of probability.So in pursuit of his "demon" he was already attempting to mathematize the incalculable, the indeterminacy assumed by human projective "freedom, the Epicurian "swerve."