We have a very large barn on the property and I would like to use one of the rooms inside the barn and convert it to a home cinema.
I won’t be adding any extra windows to the barn.
All I will be doing is concreting the floor and dry lining one room inside the barn and then installing a video projector and some seats.
It is the sort of thing I would need planning permission for?
Personally, I’d go and ask to see your Mairie’s special person for that sort of thing. Ours comes under the category “Référente solidarités, urbanisme et secrétariat du maire”. We asked her advice about a wooden terasse we were adding onto the house and she told us what sort of permissions we would need and gave us the forms.
It all depends on what your barn is currently labelled as, officially, and he/she will know. You may not be permitted to do it at all if it’s in some sort of “agricultural buidings only” zone, or you may need a declaration préalable,or planning permission, or nothing at all! Also depends on how big this home cinema is going to be…
And whether you are going to sell tickets, ice cream and popcorn, presumably. 
You are changing the use of the barn, from agricultural to what could be classed as habitation as even if not actually living in it it could be considered a liveable space. And with some barns a changement de destination is impossible, with others it needs permission - depends on local plan, zoning and politics.
You could of course say you were insulating it to watch your crops ripen….
Technically it depends on a few points…
You will be converting part of the barn into a living space, so the Mairie will need to give permission, whether a declaration préabable or permit de construire.
If your living space is 150m² & over (used to be 170m² you will need an architect (silly as this seems) to sign off the plans.
Before any works can start you’ll need to ask for a change of use from agricultural to habitation or un ERP if you plan to gain money from the home cinema from the public, this may include though I’m not sure if this is the reg’s for an association.
Then the impots will be notified so you’ll pay more tax.
Unless it’s a listed building nothing stopping you from putting in a concert floor and dry-lining the walls or putting in a few sockets and lighting in a barn.
There are large screens in modern milking parlours 
That’s what we’ve done with ours. Still classified as agricultural though - it’s down as a woodstore I think.
No playing with udders in the back row please.
There’s two ways to think about it.
To be habitable space it needs windows and heating. If there’s no fixed heating and no windows it can’t be habitable. Nothing to stop you tidying up the barn or storing your sofa and screens in there… But you can’t then claim it as a cinema room when you sell. It’s just a posh barn.
Or you go down the permission route make it habitable - everything Wozza said - then it’s a cinema room when you sell.
as some have already stated in this thread… the best advice is to visit ones Mairie… and discuss… situations will vary… and one’s local Mairie will know what’s what for that area.
My own Mairie has asked me to pass the word to our local Brits… to please discuss any project/plan of action… Before doing anything… and certainly before spending any money on materials/whatever…
I have passed the word and after that it’s up to the Brits to do things properly… 
You have Brits ? We had an American, but he died recently aged 98. We have some Belgians, but there’s is just a MS and nobody likes them.
there aren’t many… and they are far-flung across the commune rather than here in the village 
…
I think you are mistaken about the purpose for which you intend to make improvements. Surely you really mean that you wish to concrete the floor and insulate the walls in order to create a dry and frost-free place in which to store vegetables for the winter months. You’ll probably need some lighting so that you can see whether you are putting turnips or potatoes into your bag to take back to the kitchen, and then you’ll need a power point or two for a dehumidifier in the event of a very wet winter that seems more likely to occur as the climate changes.
Subsequently, you might find it a convenient place to store an old sofa or armchair, or even some electrical equipment, but that is sort of by the by at some future time.
There are times when discretion is the better part of valour, and no-one has ever said ‘no’ to a question that was not asked.