What is unique about Paris' roman ampitheater, the Arènes de Lutèce?

It is Wi-Fi accessible.

Thanks to the current municipal government, twenty-first century spectators can download Ultimate Fighting bouts for free where their second century ancestors watched gladiators and animal fights along with some classical theater but also a lot of low-brow comedies.
Bird's eye view of the rebuilt arena

Built in the 2nd century A.D., the amphitheater was rare in having a stage with a two story backdrop on its eastern end and a retractable canvas roof to shade spectators in bad weather. Estimates for the seating capacity in the arena range from 10,000 up to an implausible 17,000 spectators. At the time, the entire population of Lutece, as Paris was then called, hovered around 10,000 people.(1) Roman garrison included. (Like the seating of the arena, the size of Lutece’s over-all population is also a source of historical dispute with some estimates rising as high as 20,000 inhabitants in 2nd century.)
Not a bad stadium for a provincial town

To fill all the seats (slaves and women were relegated to the nose bleed sections), major spectacles were needed. Productions likely included fights between bears and dogs, horses versus wolves or whatever beasts the traders brought in which may even have included a lion or two. Large scale gladiator fights like in the movies would be rare as they were expensive, however the arena did host at least one naval battle with water piped in from the near-by Bievre river which today feeds the neighborhood sewer system. Paris’ Cluny Museum which houses the ancient roman baths where spectators could wash up after a good bloodletting, has a small ivory panel depicting one popular show; a man trapped inside a large wooden framework ball rolled out to wild bears who would presumably smash it to pieces to get at the meat inside.
Bear with the large size photo (pun intended), to fully make-out the different blood sports. The bear attacking a wooden ball with a man inside is at the top of the arena scene. The hoops being thrown around are a mystery. 

There is a very slight chance that the Christian martyr Saint Denis was decapitated here around 250 A.D. and not a couple miles away on Montmartre (Martyr’s Mountain). Probably some Christians did die here, if not fed to lions then to wild dogs or seasoned gladiators like the one whose helmet adorns the front entrance today. Unfortunately nothing remains of the original arena as it was reduced to rubble by the end of 4th century. The ruins were discovered in the mid-1800s while workers were digging up the plot to make a tram station. Thanks to Victor Hugo’s urging, the city moved the trams and rebuilt arena into the popular and Wi-Fi accessible park it is today.

Fun then

and today

(1) L C. “La population de Lutèce avant 275 après J.-C”. Population, Année 1962, Volume 17, Numéro 2 p.327-328. 2008. Persee Scientific Journals. 21/08/09. http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_1962_num_17_2_10103