First thing to do would be to draft a freelance contract and be careful that you exclude any compensation/benefits that may make it so courts see this person as an adjunct employee. Things to watch for are exclusivity, offering benefits or the ability to buy into benefits, providing equipment, not having a term to the contract with renewable dates.

Second, you need to terminate the current employment contract and have it signed off by both parties – pay out vacation pay, etc. You do not want to pay severance, so it is critical that the employee signs off and doesn’t feel like the freelance contract is being forced on them or is contingent to them signing off. We would recommend that you are clear and say we cannot continue your employment without a valid work visa, we’d like to continue working with you, we can offer you this contract as a freelance contractor moving past the date of your visa expiry.
You may also want to investigate you tax obligations to this point. An employee living and working remote in France is required to pay French employment taxes, as is the company employing them. You may have been flying under the radar, or you may already be meeting your French obligations, I don’t know, but the payroll contributions for France are considerably higher than that of Canada, and more and more EU countries (with the exception of Portugal) are going after employers with remote employees working as digital nomads in the post COVID landscape.