Employers can terminate an employee for any reason or no reasons as long as it is not a prohibited reason such as discrimination based upon race, religion, gender, sexual orientation, military service, disability, etc. or in retaliation for reporting illegal conduct.
Your question does not suggest an illegal motive for your termination.
Employers are free to fire their employees based on false information or belief, so no claim for wrongful termination would arise from the facts you have described.
The above noted, if you can prove that the store promoter lied about having seen you steal, you may be able to sue them for defamation. However, you as the plaintiff would bear the burden of proof and it would seem your employer can at least partially corroborate the allegations against you. Seems like quite the uphill battle to me.
This answer is a general interpretation of the law and is not fact specific to your case. Likewise it does not create an attorney-client relationship. You should seek an attorney for a review of your specific facts and documents.
First, you can be terminated for any reason, or even for no reason. You can be terminated based on the lies of co-employees, for irrational reasons, unreasonable reasons and unfair reasons. There is absolutely nothing you can do about this unfortunate situation.
Second, your final question was whether you could sue the person who falsely ratted on you. The answer is yes, you could, if you could prove that she made an objectively untrue statement of fact to your employer with the intent of getting you fired. Of course, proving that is a virtual impossibility. At best, it is a he said she said situation. You likely cannot prove your case by a preponderance of the evidence under those circumstances.
Good luck to you.
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Like my colleagues said, California is an at-will state. That means that there is a presumption your employer can fire you for any reason or no reason at all. There are some exceptions to at-will employment. Terminations that fall under these exceptions are "wrongful terminations." Wrongful termination law normally requires that there be some sort of a breach of an employment contract, or breach of some important public policy such as termination based on some sort of harassment, discrimination, or retaliation. However, you have not indicated any such basis.
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