Without a withdrawal agreement
British citizens will no longer benefit from the rights and obligations as regards residence and employment in France reserved for EU citizens. As from the withdrawal date, you will be subject to non-EU law.
If you are a legal resident of France prior to the withdrawal date, you can apply for a residence permit marked with the term "temporary worker". This is the only residence permit granted to posted workers. This residence permit will allow you to live and work as part of your posting to France after the grace period provided for in the Order. This period will be determined by decree at a later date, and will be between 3 months and one year. With this type of permit, you do not need to apply for a work permit.
If you are posted to France after the withdrawal date and you are not a legal resident of France before this date, you are not eligible for this residence permit under the conditions stipulated in the Order of 6 February 2019. In this case, you will need to apply for a residence permit that corresponds to the reason for your presence in France (posting), under the ordinary rules applicable to foreign nationals. If the posting is intended to last less than three months, you do not in principle need to apply for a residence permit.
Except in the case of certain activities, you must apply for a work permit to carry out a professional activity as an employee in France, including as part of a posting.
Prior to the start of your posting, your employer must declare your posting as well as the service to be provided in France using the SIPSI portal (http://www.sipsi.travail.gouv.fr) avant le début de la prestation.
The rules on posting to Europe will no longer apply. Your employer must now register you with the social security system of your place of work (in this case, France) and declare you to URSSAF. Depending on your nationality, you must ensure that you meet the condition of the lawfulness of your residence in France and contact your local national health insurance office to take the necessary steps.