Legal Question in Business Law in California

Employees in California generally are at-will, which means they may quit or be terminated at any time, for no reason or any reason, except illegal reasons. There are insufficient facts to determine whether it was an illegal reason. Depending on the circumstances, you might have a claim against the person who made the false allegation.

Apparently the employer believed the allegation, false or not. More facts are needed, but if the employer acted in a good faith beleif that the allegations were true, it was probably on solid ground, even if it is ultimately proven that the allegations against you were untrue.

Legal? Yes. You're an 'at will' employee that can be fired any time for any reason, unless it is 'discrimination' based of race/age/sex/etc.