Word/term for "the ability to affect history or make things happen"?

Solution 1:

Orenda

The force of human will, in opposition to fate or destiny, to affect the world.

http://dictionary.reference.com/browse/orenda
a supernatural force believed by the Iroquois Indians to be present, in varying degrees, in all objects or persons, and to be the spiritual force by which human accomplishment is attained or accounted for.

http://www.merriam-webster.com/dictionary/orenda
extraordinary invisible power believed by the Iroquois Indians to pervade in varying degrees all animate and inanimate natural objects as a transmissible spiritual energy capable of being exerted according to the will of its possessor

http://www.urbandictionary.com/define.php?term=orenda
a supernatural, divine force within every human being. Always omnipresent. It empowers people to change the world in a positive, loving way. It is the energy that effects change in One's own life. "That inspirational speaker lifted me up so much with her 'orenda'. She made me feel that energy within myself to change the world for the better, through changing myself."

http://io9.com/5905257/10-untranslatable-words-and-when-youll-want-to-use-them
the invocation of the power of human will to change the world around us. It is set up to be the opposing force to fate or destiny. If powerful forces beyond your control are trying to force you one way, orenda is a kind of voiced summoning of personal strength to change fate.

http://www.oxforddictionaries.com/definition/english/orenda
invisible magic power believed by the Iroquois to pervade all natural objects as a spiritual energy.

Also see Google results for "orenda definition"

Solution 2:

I think influence may suggest what you are referring to: (from TFD)

  • A power affecting a person, thing, or course of events, especially one that operates without any direct or apparent effort:

Charisma:

  • a special personal quality or power of an individual making him capable of influencing or inspiring large numbers of people.

Probably a mix of the two characteristics can define what you are looking for.

Solution 3:

Je ne sais quoi comes to mind as a loan phrase. It is used as a certain something in English also. [I first didn't realize that you mentioned this French term in the question but I explained, in detail below, why it is a good fit.]

Another term that comes to mind is x-factor (also x factor).

As you can see in the examples below, there are also terms like leadership presence and executive presence that are used in certain contexts. Though, you can apply x presence to different contexts. For example:

The “star presence” of great actors is one of the most compelling and powerful aspects of the movies we love.

http://www.movingimage.us/films/2014/07/20/detail/star-presence-on-screen/

You have a variety of examples from different contexts, so that je ne sais quoi or x-factor is a better fit. (Details follow.)


Je ne sais quoi

An intangible quality that makes something distinctive or attractive.

She has a certain je ne sais quoi about her.

http://en.wiktionary.org/wiki/je_ne_sais_quoi

From Wikipedia's Leadership article:

None of the old theories successfully address the challenge of developing "leadership presence"; that certain "something" in leaders that commands attention, inspires people, wins their trust and makes followers want to work with them.

From an article titled "The Five Greatest Superpowers of Moderator Superheroes":

There's no other way to put it – some people just have a super ability to charm an audience, be it with wit, personality, manners, or a combination of all these things. You can choose a moderator who seems like a perfectly nice girl or guy, but by finding someone with that je ne sais quoi, that extra skill to win over the audience with their natural style, you're ensuring a valuable bond between the attendees and the moderator.

http://adage.com/article/btob/greatest-superpowers-moderator-superheroes/290646/

From an article on Financial Post:

Executive presence is easy to see but hard to define, which may be why there is precious little in today’s voluminous literature on leadership indicating exactly what it is or how to acquire it. Do a Google search and you’ll find articles that talk about confidence, communications, appearance, maturity and other factors but that aren’t much more helpful than that. It’s what the French call je ne sais quoi.

http://business.financialpost.com/2013/04/29/executive-presence-the-other-reason-business-leaders-are-asked-to-leave/


X-factor

a special quality, especially one that is essential for success and is difficult to describe

http://www.oxfordlearnersdictionaries.com/us/definition/english/x-factor

X factor means some advantageous quality that someone or something is attributed to have, a quality that is regarded as mysterious and difficult to describe or isolate.

http://encyclopedia.thefreedictionary.com/x+factor

Below is an example in a business context:

Most of us have watched it happen in the workplace. There’s a go-to person in the organization who gets everything done. Never misses a deadline, never forgets a detail, but never gets promoted into a senior position. Meanwhile, others break through to the next level. Leaders listen to them; subordinates recognize their authority. What do those people have that the other highly competent manager lacks?

In the corporate world, that missing ingredient is often referred to as executive presence. Most people recognize it when they see it, but quantifying it is almost impossible.

Essentially, these people possess the business "X factor.

http://www.psychologytoday.com/blog/you-according-them/201302/do-you-have-the-leadership-x-factor


Bonus: http://tvtropes.org/pmwiki/pmwiki.php/Main/JokerImmunity

Solution 4:

Greatness is the term that comes to my mind.

exceptionally high quality <a poet whose work is of enduring greatness>
(Source: Merriam-Webster)

It is an established term to refer to people that appear to be innately better than everyone else.

Greatness is a concept of a state of superiority affecting a person, object. Greatness can also be referred to individuals who possess a natural ability to be better than all others. ...
(Source: Wikipedia)