Hi Bev, thanks for the information!
So, let me try to get a clear picture of this.
1. What do I need to apply for, or get before comming over and staying for a year - a residence permit or residence visa? And, how and where do I get these papers?
You apply for a "long stay visa" - for which you must have a convincing "reason" to want to live in France and the means to support yourself. Check the website of the French consulate covering the area where you are now resident. They indicate what documents you'll need and how to apply. But they all have a caveat stating that just because you have all the documents they ask for, it doesn't necessarily mean you'll be granted the visa.
2. I have heard about the "carte de sejour", but do not know exactly what its for. As I understood, I was to get this after being in the country, correct? Do I apply for this along with the residence permit or visa, or after?
A visa is a document allowing you to enter the country. (Though, like for the US, the immigration people at the border can deny you entry even with a visa, if they suspect your motives or anything else.) Once you have been admitted to the country with your visa, you then follow the instructions of the OFII (one of many offices involved with immigration) as to whether you have your visa "validated" as a residence permit for your first year in France, or just apply to your local prefecture to get a carte de séjour. During this first year in France, you'll be expected to take a couple day-long classes on "Life in France" and to learn the language, if you don't already speak, read and write it.
3. What if I own the company I work for.... how do I sponsor myself? I can do my work in France through my computer, which is not really working in France..... so I am just staying there. Are you saying that I have to pay taxes there by doing this?
Now, you're getting into very murky territory, as there isn't a tried and true path for entering France to set up a company, as it seems you are planning on doing. If you are resident in France doing work through your computer anywhere in the world, you are "working in France" for tax purposes. (And again, like the US, France taxes based on worldwide income.)
4. As I understand, a landlord will not rent me an apartment until I have this "residence visa" in hand..... and a local sponsor? Please help on this one, as I was going to try to set something up before going over but maybe they wont until they see the actual papers?
This is another tricky area. With the most recent changes in visa requirements, we're hearing that the consulates are insisting that you have "proof of a place to live" (i.e. a lease in your name) as part of the visa application process. However, most landlords will not rent to someone without proof of employment, income, etc. What some folks have reported doing is contacting a rental agent and getting an "agreement to rent" - basically a document saying that, assuming the person gets their visa, the agent or landlord is convinced of their ability to make the rent payments and would be willing to rent them one of their available properties. Again, you probably need to talk to the consulate to see just exactly what they expect here.
Now, back to your basic problem: going over to France to set up a company for yourself is a bit outside the box, and thus will cause all sorts of problems when it comes to visa issuance, etc. (France is like that - you get used to it after a while.) Your best bet would probably be to make a series of short trips over to France to contact the appropriate professional people - attorney, accountant, maybe someone to function as a temporary manager for your company until you get up and running - and to get the company started.
It really depends on the type of company you're trying to set up - but in general, you won't be given a visa to set up an auto-entrepreneur business (the new, simplified business registration). You might get away with going for one of these new "competences and talents" visas if you can demonstrate that your business plan offers something of value to France (like employing French citizens).
Cheers,
Bev