I just re-read this question and noticed that I had overlooked the key phrase "without moving in there with my spouse." This narrows the question somewhat.
It does still leave open the possibility that you wish to move to one of those countries without your spouse. This should in general be possible if you have established "long-term resident" status under directive 2003/109/EC. (The French term is résident de longue durée.) Without that status and without your spouse, you would not have any easier path to a residence permit in any of those countries.
I suppose, however, that the most likely intention behind your question is to be able to work as a self-employed individual for clients in the named countries while remaining in France with your spouse. This would normally fall under freedom to provide services, but there are several possible points of confusion or ambiguity.
Here I should note that I am not a lawyer, and I am more knowledgeable about free movement of persons than about freedom to provide services, so take all of the following with a grain of salt, as it were. It is intended as an introduction to the legal context to help guide you in doing your own research.
First, if you're doing the work in France but some of your clients are in other EU or Schengen countries, you do not need to concern yourself with the right to work in those countries because you're not actually working there. Even going to those countries for meetings with your clients would be a visit for a business purpose rather than work.
You can think of it this way: if it's something that you could do while living in India, you can do it while living in France. If any travel to your clients would be permissible with a short-stay Schengen visa as a business visitor, then you can undertake the same travel without any additional authorization thanks to your having a French residence permit.
Second, if you're traveling to another EU or Schengen country and actually providing your service there, this should be permissible under freedom to provide services. In such cases, the business you're engaged in should legitimately be a service provided to a client and not "bogus self-employment" (this phrase comes from directive 96/71/EC). Whether a relationship with a client is actually an employment relationship probably depends on the national law of the country where the work is being performed.
Switzerland is a slightly different matter because it is not part of the EU. Instead, it has concluded several agreements with the EU with similar provisions, but not identical, and it exercises somewhat tighter control over these matters. There is a notification procedure for short-term workers subject to some minimum amount of time, but it seems that self-employed third-country nationals are excluded (expand "Notification rules" and then "How to submit notification forms"):
The following categories of individuals are authorized to work in Switzerland for up to three months or 90 days per calendar year by virtue of the notification procedure:
- EU/EFTA nationals who have been employed to work in Switzerland by a company based in Switzerland for a period of up to three months
- Posted workers from a company based in an EU/EFTA member state, regardless of this worker’s citizenship. Third-state nationals, however, must have been admitted permanently in a labour market of an EU/EFTA member state before being sent to Switzerland. Generally speaking, this criterion is deemed to have been met if the individual has held a standard or permanent residence permit in that country for at least twelve months.
- Self-employed service providers (EU/EFTA nationals) based in an EU/EFTA member state
So it may be that to have access to the Swiss market you would have to set up a separate company in France. (But remember that business visits such as meetings to support services that you provide remotely from your normal place of business in France probably don't trigger this requirement; it should only apply to work that you actually perform in Switzerland.)