Chris,
As far as I can see, the Orleanist claimants to the French throne mostly styled themselves as 'King of the French' when they succeeded to their father's claims. During their father's lifetime, they were usually styled Duc de Chatres, Duc de Guise or Comte de Paris. I suppose that the Duc d'Orleans title was inherited from Louis Philippe, and was only held by the man who claimed to be king, and if he was calling himself King he would not use the Orleans title. His children, though, would be styled d'Orleans - e.g. Princess Isabel d'Orleans, and they are known as the House of Orleans.
The late Henri, Comte de Paris (1908-1999) the second most recent claimant, always styled himself by this title, though I don't really know why he never called himself King. His son Henri (born 1933) is the current claimant, now calling himself Comte de Paris and Duc de France.
So, in answer to your questions, there is no Duc d'Orleans today, though the Comte de Paris may consider it one of his titles.