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There's no such thing as a "tourist visa" or a "business visa" for France. You apply for a uniform short-stay Schengen visa, and there's only one kind of that.
When you apply for such a visa, there's a question on the application form asking for your main purpose of going. Business, tourism, and so forth are different answer choices for that question -- but they will NOT lead to different types of visa, or trigger different legal rules.
The question merely serves to help the processing of the application, and to help avoid pointless differences in phrasing between applications that do fit neatly into one of the common cases. (For example, if there was only a free-form field, some tourists would spend energy worrying about whether to write "tourism", "vacation", "pleasure", etc. for no good reason. As it is, they can simply check the provided box).
You should be completely fine with ticking the "business" box. That does not, as you seem to suppose, imply that you're necessarily traveling on behalf of an employer, or for doing any particular commercial activity.
But if you can't bring yourself to do that, just tick "other (please specify)" and explain in your supporting documentation what the deal is.
The actual Schengen legislation that consulates must follow when deciding an application does not distinguish between the various purposes of stay. The rules just uniformly say that you must convince the examining officer that you're not going to be an illegal immigrant, that you have the means to support yourself, and so forth. In order to do that you need to show that you have plans for your trip that make sense, in whatever way you have to show that.