I agree with Robert.
I have done it in both countries. France is a bureacratic nightmare. Company tax is 33% and UK is 20% and reducing each year. If you are UK based, then you can easily open a UK company.
You can trade in France etc but you don't charge VAT/TVA if you issue invoices. Your clients in France when they do their TVA returns have to state this and pay TVA direct in France. Conversely, you cant claim VAT deductions in the UK on your purchases or invoices that you incur. If you live in France, then your personal earnings from the company have to be declared there.
After April 2016 the UK fell into line with France in the way that company earnings can be paid to the company owners. In years past, it was possible to avoid NI / Social charges by paying via dividends but this is no longer the case. There is a lot more cohesion between the two.
If you are not sure of your earnings, and they are likely to be meagre in the beginning, then you could try French Autoentrepreneur. You need to be resident in France, and it is limited to 3 years.
I use a UK Accountancy firm who cost a lot less than the French-based international one that I used who had no added value whatsoever. I would advise to stay clear of larger accountancies.
I don't know how you would go in France for a company account if you register in UK. I opened a euro account with HSBC in UK but it is expensive if you have a lot of small transactions. Once per month I "swept" the account via a currency house into pounds and used that for pound value for declarations in UK.
I've since stopped doing France work and to be honest, life is a lot simpler. It is complicated and if you don't have the turnover to merit it, it isn't worth the bother. Operating as owner-operator is easier, but in France you will lose around 50% in charges, URSSAF for example will still charge (or they used to) on a 0% turnover.