Hi Jemima, well done on doing so well, I too have changed up from AE due to exceeding the limits. I knew this was going to happen so made lots of enquiries including visiting the man in charge of the Service des Impots des Societies who was exceedingly helpful. You do not have to charge TVA the year you go over the threshold, you also do not have to register the following year either. He explained that many companies do well one year then drop a little the next so you are only obliged to register when you exceed the limit two consecutive years.
I went ahead with my enquiries and everyone kept telling me that I would have to register, so went back to Mr Helpful and asked him to clarify as everyone else kept telling me I had misunderstood. No, he said, it's very simple, you may choose to register at any time but only obliged to when you exceed the limit two years.
I'm explaining all that because if you live in France and your work is carried out in France, France is considered your main home regardless of how many days you spend here. I believe you also have children registered in school here so therefore you are definitely considered to have your main residence here and as a sole trader must register your company here.
What Claire explains is still correct and it is not pleasant to be hauled through the judicial system by the fiscal authorities. I know someone it happened to recently even though the person spent a great deal of time in the UK where they had a limited company with international clients (no French at all) the fact was the court decided they lived here and must register and pay here.