Hi there Lewis.
Firstly, you are correct to suspect that two individuals living at the same address and each registering as micro entrepreneurs in the same activity, would not be acceptable or legal. If you work with a partner then neither of you is genuinely an “entreprise individuelle” ie a one-person business. You need to set up a business structure suitable for a partnership. Your registations would be unlikely to be processed and if they did slip through there is the danger it would be picked up later on, because the registrations would in themselves suggest you are working in partnership, and an inspection of your accounts would confirm it. You would then be “re-qualified” and expected to retrospectively pay the charges you’d avoided. Explained here https://www.portail-autoentrepreneur.fr/actualites/possibilite-association-auto-entrepreneurs
Your case would be further complicated, as David says, by the fact that in fact neither of you is genuinely self employed. Claiming to be self employed when in fact you work for one company is known as salariat déguisé in France and URSSAF deals with it severely; I believe the UK has the same concept of “disguised employment” but HMRC is less proactive about stopping it.
So one way and another, registering as micro entreprise could lead to a lot of trouble in the long term.
One correct route would be for your UK company to register you with URSSAF as employees based in France. This would involve putting you on a French contract that complies with French labour laws, issuing French payslips each month and paying the appropriate social security contributions. URSSAF has produced a booklet in English to explain the system https://www.urssaf.fr/portail/files/live/sites/urssaf/files/documents/5015-GuideCNFE-UK-2017.pdf and has set up a portal to guide you through the process https://www.tfe.urssaf.fr/tfewebinfo/cms/lang/en/presentation.html
I think this would be your best route if you will in due course after Brexit need cartes de séjours, because having the status of French employees with full employer/employee contributions paid, is pretty much the gold standard; the fact that you’re employed by a UK company shouldn’t make any difference as long as you’re properly registered with URSSAF. The downside of course is the level of cotisations your company will pay.
Otherwise, there are no doubt various ways you can do this by setting up a separate business in France (SAS, SARL or whatever) to work in cooperation with your UK company, you would need to talk to an accountant or business consultant about this. Alternatively unless there are reasons why you need to have a UK Ltd Co, it might be simpler to close that down and move the whole business to France. to avoid having tax liabilities in both countries. You would then have the choice between employing yourselves as salariés, or being gérants non-salariés (TNS-travailleur non salarié). As TNS you pay lower social contributions and have more flexibility. But you could only be TNS of a French company.
Hope this makes sense and gives you an idea of a way forward. Can we take it you’re confident that Brexit won’t end in no deal, or does one or both of you have an EU passport?