Contact the AVS service des independants directly, they'll be better able to advise you. As far as i'm aware you need to have multiple clients. I was required to send contracts as proof to register.

https://www.ocas.ch/particuliers/cotisations/independants/

https://www.fer-ge.ch/web/fer-ge/le-statut-d-independant

I agree with the other comments and would just add if you only have one revenue stream, they consider you an employee of that company. If the Belgian company wants you full time, can't you just become their employee? 

I can imagine that they are doing that for tax reasons. But this is not our problem. 

As far as I read you can be self-employed in Switzerland. Having one client is a problem, but I believe it's your problem as entrepreneur. as long as you are having the sufficent ressources to live here (and of course don't say the same thing as you said here, because it will look weird). 

Let's say you want to be a self-employed, a consultant.

Geneva has a page for that;

http://ge.ch/population/prestations/activite-independante 

In french from the Federal administration: (link here: https://www.sem.admin.ch/sem/fr/home/themen/fza_schweiz-eu-efta/eu-efta_buerger_schweiz/faq.html )

Les travailleurs indépendants ressortissants d’un Etat membre de l’UE-27/AELE doivent, dans les 14 jours suivant leur arrivée en Suisse et avant de commencer leur activité, s’annoncer auprès de leur commune de résidence, de l’autorité cantonale de l’emploi ou de l’autorité cantonale compétente en matière de migration (selon les cantons) et demander une autorisation de séjour en vue d’exercer une activité indépendante. Il y a lieu de présenter une carte d’identité (ou un passeport) en cours de validité, de même que les documents prouvant que les conditions pour travailler en tant qu’indépendant sont réunies (capital de départ, éventuelle inscription au registre du commerce, etc.). L’exercice d’une activité lucrative indépendante ne peut commencer qu’une fois que la demande a été acceptée / l’autorisation a été délivrée.

Les autorités cantonales compétentes en matière de migration vous fourniront davantage de renseignements à ce sujet :
Autorités cantonales des migrations et de l’emploi

Une fois la preuve acceptée, une autorisation de séjour UE/AELE d’une durée de validité de cinq ans est délivrée. L’autorité compétente peut toujours, par la suite, contrôler si l’activité indépendante est effective et durable et si elle permet à l’étranger de subvenir à ses besoins. Si tel n’est pas le cas, l’autorisation peut être révoquée.

Des informations générales sur les créations d’entreprises sont disponibles sur :
Portail PME pour petites et moyennes entreprises

Good luck!!!!

It looks like I was in a similar situation to you.

I worked full-time for a UK based company as an independant contractor (not self-employed, this is something different)

This was because my employer did not have a presence in Switzerland and therefore could not payroll me through another country.

I worked for 10 months like this in the end, so I don't know if you are working indefinitely for your company in Belgium this would be the same case or not.

In my situation, I had to send my contract to the Social Security office www.ocas.ch and had a fiduciaire do the tax return for income tax.

As far as I understood, it is possible to work as a "detached" person indefinitely for one company as long as OCAS is being informed. I also had to send a letter to the Cantonal Tax office to inform them that I was working as an Independant person but I don't think they did much with this information!!

Feel free to contact me if you need any more information.

You should as the others said go to ocas or to any other social security company. I do not think it will be called independent but it will probably be like those people who are contractors at the UN and want to pay social contributions and taxes.

Thank you all for the replies! 

In the meanwhile, I visited 2 independent accountants, and especially Michael Parrat -CMAC accountancy- was very helpful in providing me a lot of information. 

The proof of multiple income sources would pose a problem, so he suggested to become a "swiss representative" for my company, which I assume is what you described above as an independent contractor. It would suffice to notify a social security company, such as OCAS. 

Through this arrangement, the employee would remain with around 75% of his gross salary after contributions and taxes (calculated for a monthly gross salary of 6000 CHF).

However, I think I would want to opt for the self-employment contract, in order to widen my options to additional business activities. I'll look into the websites listed above, thanks.

How are your experiences with co-working spaces? 
I have visited Voisins, and walked by Cric Crac Croc. Anyone have experience with one of these?