Moved to France, self employed and need healthcare?

We have recently moved to France in the last month. Myself and my (French) wife have an Irish company which sells children’s toys online in France and in Ireland. All the work, warehousing picking/packing etc., is carried out in Ireland so I understand the company isn’t liable to French taxes/social charges etc. What are the implications of us taking a salary from the company… would we be liable to French taxes social charges? What would be the most efficient way of us taking money from the Irish company?

Assuming we are not paying French social charges, I presume we wouldn’t come under the Securité Sociale? What other option is there for us? Is there any way for us to be part of the French Health system? Can the CMU apply to us?

Currently, we have private Irish medical insurance which I have been told will cover us in France for what we would be covered for in Ireland. We have 2 children and a third on the way, can we apply for Allocations Familiales, etc. We are only here a month and have not made a Declaration d’Impots in France as of yet? My wife is French, whatever bearing that has on the situation. In Ireland we would be covered free of change for pre-natal care. What would we be entitled to here in France?