Is there a real unicorn horn in Paris?

Yes.

The Cluny Museum has the famous tapestries of The Lady and the Unicorn, but more importantly, just a couple rooms over is an actual full length unicorn horn from the early Middle Ages. Probably sold to a gullible royal by Danish traders using a narwhal tusk, the counter-clockwise spiraled horn was believed to hold magical protective powers against poison. Ground into powder or cut to be used as a cup, the horn would boil the liquid or sweat upon contact with a toxin. A 1593 medical study carried out on dogs poisoned with arsenic showed that unicorn horn was indeed effective as a curative.(1) Around the same time, Queen Elizabeth of England paid 10,000 pounds for one.(2)

Don't scoff. In 2008, over fifty percent of adult Americans took vitamins costing up to $23 billion total.(3) There is quite a lot of current debate whether vitamins work as advertised or not. Sort of like unicorn horn.

Maybe the question should not be if there is a real unicorn horn in Paris, but if narwhal tusk is a cure for arsenic poisoning?

(1) Goldfrank, Lewis, Neal Flomenbaum, Neal Lewin, and Mary Ann Howland. Goldfrank’s Toxicologic Emergencies. McGraw-Hill Professional: New York. 2002. pg 4.
(2) Nweeia, Martin. (Principle Investigator). “”Narwhal Tusk Research”. 2003. Arctic Studies Center. 09/08/09. http://www.mnh.si.edu/arctic/html/narwhal.htm#top
(3) Parker-Pope, Tara. “Vitamin Pills: A False Hope?”. Feb. 17, 2009. The New York Times. 09/08/09. http://www.nytimes.com/2009/02/17/health/17well.html?_r=2&scp=2&sq=vitamins&st=cse#