Firstly one can still be paid without the NINo as long as they have the valid RTW in the UK (your payroll team would know), and secondly i suspect they have it yet just don't know it - they should enquire HMRC themselves. Also for tax purposes i think there are certain "grace days" of some sort that one can pay tax in the UK only, something like 90 days. but i am not too sure on this part and also it is the employee's responsibility.

You also need to be aware that they are probably classed as a having residency in France so it is likely that French law considers that they are employed in France for employment law purposes. If this is the case you would need to make sure that your employment contract complies with French employment law. The organisation may also be considered to be an employer in France and as such have to pay into the French tax/national insurance equivalent system.
You probably do need to get some urgent specialist legal advice on this

In reply to Teresa:

Agree completely with Teresa. This is far more complicated than basic tax and NI questions. Any specialist advice you seek might well advise you against getting into this at all if you do not have the systems in place to employ someone based in France.

In reply to Eleanor:

Agree completely with others - almost certainly will be classed as a resident of France and if they have been living there for many years will have been employed and paid by others as such. There is no need to demonstrate RTW in the UK if the individual is never going to step foot on UK territory - but if there is an intention that they are going to relocate to the UK in future you will need to do a RTW check and make sure you have evidence that they are a UK National. If they don't have a passport, there are other options you can consider - see this link: https://www.gov.uk/government/publications/right-to-work-checklist/employers-right-to-work-checklist-accessible-version

But otherwise, do get advice ASAP!