At the end of an ESPP period the shares are yours just like any shares you buy yourself. You don't need to sell just because you're leaving your employer. (No point in putting money into the scheme starting in May though.)
Some people will make a good point that you shouldn't be heavily invested in any single stock - however that's a choice rather than anything you have to do.
It's presumably a US broker? But since your employer has confirmed you will continue to have access so at least you're not being forced into hasty action.
One thing to do is periodically log in to the account, US brokers can close the account if they see no activity for a few years then hand the shares to the state, who'll then sell them - process called escheating.
If you'd like to keep the shares for years you could look to eventually transfer the shares to a EU based broker - avoids risk of echeating, and you move away from a restricted account that may be partly under the control of your employer.