Thank you for your question. The reason for your confusion is that there is no particular visa for "freelance" work. The visa system was established before such work became a practical possibility for most people. The other reason is that freelance work is not seen positively by the state, because very easily you could lose clients and fall back on to their social security system.
The other thing is that for long sejour visas, you need to declare the purpose before you obtain the visa. You may not declare one purpose, and then do something else while in the country.
The visa which would fit what you wish to do is the "Long stay visa for commercial, industrial or artisanal activity in France".
This visa allows you to come to France, begin your activity, and within 2 months of your arrival, request a Carte de Sejour, which is the card enabling you to remain in France long-term. Specifically, you will be able to request a Carte de Sejour for 1 year, which can then be renewed and leads eventually to permanent residence.
The paperwork for this visa is quite complicated. The full list is available here (http://www.consulfrance-washington.org/IMG/pdf/Liste_Docs_Visa_LS_carte_de_commercant_creation_ENGLISH.pdf). You will need all the documents in Section A and from Section B the ones listed under "pour l'exercice d'une activite en nom propre / creation d'activite", specifically 10, 11, 12a and 13a. You will note that a rental / lease contract for the place where you wish to undertake the activity will be needed.
Note that "apply to work" is different from "freelancer". In legal terms, apply to work means employment. There are employment visas available, but you have to have an employer who offers you a secure job before applying for a visa (they need to go through some bureaucratic hoops as well, to hire a foreigner, specifically to obtain a certificate from the national labor office). You cannot go to France and work as an employee without an employee visa.
Freelancer, in legal speak, means you set up as a trader in France, based on the business plan you submit to the Embassy for the visa, register in the Trade Registry, and issue receipts to those who pay for your work, i.e. self-employed.
I hope my answer clarified matters and is useful, and look forward to your rating, which is essential to my activity.
Dr I L Vlad