Basically the first thing that you need to do is to apply for a Visa Look at these sites and it will take you through the options
France-Visas is a single portal with all the information you need to guide you through the process and help you every step of the way (preparing the application, entering details, submitting and tracking the application).
uk.ambafrance.org
Normally pre brexit you could have moved set up a French business entity registered for tax cotisations for health care etc and away you go Nwo that may all become problematic but you will need to set up something in France for your business because even if you work remotely you are still required to register for tax etc
You should note that without a Visa you can only stay for 90 days in France?/Schengen Area in any 180 days
You also need to make sure that you get the right visa for your circumstances as some do not permit to you to work
By googling "setting up a business in France post brexit I found this
Our Law Firm assists you with all your projects in France
www.startup-france.com
but I know nothing about them except they make money out of you by the looks of it but in any event I think you may need help more than we can provide on here You could also try the French Chamber of commerce
Les CCI fournissent informations, conseils et outils pratiques aux entreprises, créateurs d'entreprises, étudiants et lycéens, collectivités territoriales.
www.cci.fr
Unfortunately Brexit will affect so many Brits