If you have never been in the French system, i.e. no social security number, you will need your birth certificate when registering your business or when adding your spouse and children as healthcare beneficiaries ayant droit.
If your children were born in France, you can request this document form the mairie of the town where they were born or online. Free at here. If they were born in the UK, you can request a birth certificate online. It will cost between £25 and £60. This document will also be requested if you want to sign a PACS with your partner.