No, you are not required to reimburse the employee in this situation.
Since your company already provides reasonably adequate safety shoes, and the employee purchased expensive shoes without prior approval or following company policy, the cost is unlikely to be considered “reasonable” under Section 2802. You may offer replacement shoes from the company’s stock instead.
Because the terms “reasonable” and “reasonably” can be subject to interpretation, consulting legal counsel is advisable if there’s any uncertainty.
Read about Tools, Uniform and Equipment Explained in the HR Library.