In theory yes, your residence card should be sufficient. However, I would not try it, as the legal situation is disputed and the implementation is chaotic. You should apply for an Schengen visa under European law (according to the Surinder Singh precedence), which is issued reasonably quickly and free of charge.

Tom

 

Needing a visa is determined by your nationality and the passport you posses. Since you have a Turkish passport and Turkey is still not part of the EU, then yes you would need a visa to go to France. The good news is, since your spouse is an EU citizen, the visa for France you apply for would be free of charge, provided adequate documentation is provided with the application, and should take no more than a few business days.