Different things, first and foremost. The aim in parkour is to move as efficiently from one place to the next. The aim in free running is to use one's environment to produce a kind of mobile artistic form.

Free running is probably Ne/Si, based on the philosophy. It takes out the Se efficiency in overcoming obstacles, and makes some fun out of them.

Parkour generally interests me more. The overview on the wiki is quite interesting:

Parkour is the art of escape and a physical activity that is difficult to categorize. It is often categorized incorrectly as a sport or an extreme sport; however, parkour has no set of rules [lack of Ti], team work, formal hierarchy [again, lack of Ti, so unlikely Beta], or competitiveness [seems contradictory to Se]. Many non-practitioners regard parkour as an extreme sport. Most experienced traceurs think of parkour as a discipline closer to martial arts. According to David Belle, "the physical aspect of parkour is getting over all the obstacles in your path as you would in an emergency. You want to move in such a way, with any movement, as to help you gain the most ground on someone or something, whether escaping from it or chasing toward it." Thus, when faced with a hostile confrontation with a person, one will be able to speak, fight, or flee. As martial arts are a form of training for the fight, parkour is a form of training for the flight. Because of its unique nature, it is often said that parkour is in its own category.

A characteristic of parkour is efficiency. Practitioners move not only as fast as they can, but also in the most direct and efficient way possible; a characteristic that distinguishes it from the similar practice of freerunning, which places more emphasis on freedom of movement, such as acrobatics. Efficiency also involves avoiding injuries, short and long-term, part of why parkour's unofficial motto is ętre et durer (to be and to last). Those who are skilled at this activity normally have an extremely keen spatial awareness [something Se egos tend to have].

Traceurs say that parkour also influences one's thought process by enhancing self-confidence and critical-thinking skills that allow one to overcome everyday physical and mental obstacles. [I found this very interesting - it seems to most reflect an SLE's point of view.] A study by Neuropsychiatrie de l'Enfance et de l'Adolescence in France reflects that traceurs seek for more sensation and leadership than gymnastic practitioners.
There's evidently a lot of Se in there (I've bolded what is relevant), and it proves that Se valuers don't just want to fight all the time. More interestingly though, is the seeming conflict with Se. There is a clearly confrontational attitude in Se ego types at times, and this seems to downplay that.

I'd be interested to know what you think about this.