*drags the thread up from the grave*
Live! Liiiiive!
*lightning bolts*
Okay, now that that drama is out of the way, I'm going to unveil my utter geekdom here, and share the
reasons you can't use parkour as a verb.
As stated, parkour is a noun. However, English turns nouns into verbs all the time. The process is called zero-conversion, zero-derivation (in the case of English), or
verbification: when a language changes a word from one part of speech into a verb. For example, in English, "weird" is an adjective, but people often use it as a phrasal verb: "That guy totally weirded me out." Or email: "Send me an e-mail" vs. "E-mail me."
All languages engage in zero-conversion to a degree; English is particularly fond of verbification.
Given this, and English's propensity towards zero-conversion to verbs, why can't "parkour" be used as a verb?
Because
le parkour is a
French noun that has been
borrowed from French. French does not zero-convert to verbs as readily as English does (although this is not always the case: verbs like "googliser"=to [look up on] Google, and the like crop up in French often enough. Worth noting is that "Google" itself is a borrowing into French, however it is a weak example as it is a proper noun for a product name, like Coca-Cola or Xerox, and is therefore generally unchanged language to language. Parkour is not a proper noun/brand name.)
All languages borrow from other languages as the need arises. "Need" is generally characterized by the introduction of a cultural element from one speech community to another, for which the receiving speech community has no equivalent. For instance, answer this question: What is the English translation for "burrito"?

In the case of parkour, no equivalent for parkour existed in English speech communities, so the name was imported along with the art form. This bond was further solidified by the application of "freerunning" as a possible English translation, and freerunning's subsequent philosophical/applicational split from parkour proper. The split necessitated a linguistic distinction between the two disciplines, handily already present via the inital borrowing of "parkour" into English.
That "parkour" is a borrowed noun is significant, because English typically doesn't zero-convert/verbify borrowed words. Support for this notion has already been given in previous posts with the examples "ballet" (also French), and "karate" (Japanese).
In French, the expression would be "faire du parkour"=to do parkour. French applies the verb "faire" (to do) to many, many physical activities. It's simply a characteristic of the language:
faire du bateau=to go boating
faire de la planche a voile=to windsurf
faire du roller en ligne=to rollerblade
faire du ski=to ski (although
skier is also used as a single verb)
faire du cheval/de l'equitation=to go horseback riding/to ride horses
...etc.
So since "parkour" is a noun, verbified in French by means of a "faire construction" ("to do" construction), borrowed into English, which typically resists zero-converting borrowed words, we have no other choice but to say "to do/practice parkour" in English.
It is conceivable that in the future, English will zero-convert parkour into a verb; but in general that will depend much on whether it gains wide acceptance among English speech communities (to me, personally, it just sounds wrong, but that may be because I also speak French).
It is unlikely that French will verbify "parkour" for two reasons: one, because it is already in wide use with a faire construction, and two, because the noun "parkour" itself derived from the French verb "parcourir,"=to run across or through. So the verb "parkour
ir" is already taken (phonetically); "parkour
er" might take root, but it's unlikely. The root verb is "courir"=to run; part of a specific verb class (-IR verbs like dormir), and although most verbification in French classifies verbs in the -ER verb class (the most common verb class), it is highly irregular/unlikely for a verb to "jump classes" like that.
So there you also have an actual linguistic explanation, and you probably also think I'm a huge nerd... which I am.

B.A., Linguistics, University of Wisconsin, 1998
*bows*