Do you have a right to see the video? No, there is no such right. Also, it's not unlawful to fire an employee without performing a proper investigation of alleged misconduct, or based upon a mistaken belief that the employee committed misconduct.

If there is a foundation for a wrongful discharge claim, such as unlawful discrimination based upon gender, race, age, color, religion, disability, and the like, you can consult a plaintiff-side employment lawyer for a review of the case. The video footage would be available during the discovery phase of any litigation; but you need to keep in mind that the files may not be maintained for very long, and by the time of any EEOC report or lawsuit it may be gone, so don't delay in seeking that review.