idée / Idée – république / République – dieu / Dieu – justice / Justice – mathématiques / Mathématiques – art / Art… et donc aussi :

histoire / Histoire…

It’s just common use in French to make a difference between some thing itself, in particular, and the concept of this thing.
Even more when, in whatever idealistic system it can be understood as some transcendant value.

l’Histoire = The concept, the Idea of history, history in general.

In your particular example, if history just stands for what happened to Jade during her life, in other words, her history in particular… then lowercase with no doubt!

Nota : In order to explain some misunderstood comment as part of the OP… of course… the difference (lowercase/uppercase) is the result of a… value judgement, your judgement regarding the value of the history you refer to. 😉

As aCOSwt said, the difference is mostly a matter of judgement, implying some common sense. In your situation I wouldn’t capitalize as this is merely not something that would end up in History books.

The following paragraph explains it quite well:

C’est le cas lorsque l’on parle de l’Histoire avec un grand H. On parlera d’une histoire pour quelque chose qui se raconte sans déférence, une histoire drôle, une histoire du quotidien. On parlera en revanche d’un personnage entrant dans l’Histoire, celle que l’on se raconte avec admiration et respect, que l’on apprend à l’école et qui se transmet au cours du temps.

This also demonstrates an idiomatic expression used to capitalize the word in a speach: “L’Histoire avec un grand H”

Here is the article from which I took this quote. It expands a bit more on the capitalization of other words.

I would expect the same basic rule can apply to other languages though:

…the most important is I got my job back, all the rest is history

Vs

Leaders of the world should have learned lessons from History

I’m not entirely sure if my sentences are idiomatic in English but I guess by now you get the nuance.