As a French national, I can confirm this is used in France in the same way thus making the same mistake. From personal experience only, I would assume it’s recent (after 2000) as I’ve been using it for some times. My parents and other family members always told me that in the context I was using it, it made no sense at all. I used it to emphasize or to implicitly say “véritablement” (truly).

Borrowed from the latin word litteralis, from literra (letter), the adverb, authentified around the mid-15th century, means what is understood “word for word”.

Looking at two renowned French dictionaries and two other sources, I found this:

Larousse

1) D’une manière littérale, à la lettre : Traduire littéralement.

1.i) In a literal way, to the letter: Translating literally.

2) Absolument, tout à fait : Il était littéralement épouvanté.

2.i) Absolutely, exactly/entirely: He was literally terrified.

Littré

1) D’une façon littérale. Traduire, expliquer littéralement. Il ne faut pas prendre littéralement ce qui ne se dit que par métaphore.
“Rousseau, dans tous les soins qu’il prescrit à cet égard [au sujet de l’enfance] ne fait que suivre exactement le système de Locke ; il est vrai qu’il ne le cite pas, mais il le copie littéralement”, [Genlis, Adèle et Théod. t. I, p. 85, dans POUGENS]

1.i) In a literal way. Translating, explaining literally. One should not take literally what is only said through/via metaphor.
“Rousseau, in all the care he gives in this regard [in regards to childhood] is only following exactly the Locke’s system; it is true that he’s not quoting him, but he is copying him literally” , [Genlis, Adèle et Théod. t. I, p. 85, in POUGENS]

The Centre National de Ressources Textuelles et Lexicales (the national centre of textual and lexical resources) also mentions it can be used as a synonym of “absolutely”: “Some time ago, when I had nothing, literally nothing, after having eaten for next to nothing, I was still lounging in my gondola” (Histoire de ma vie (Story of my Life), Sand). Far from any hyperbola.

L’Academie Francaise (The French Academy) has a section on “literally” where it warns not to use it as a superlative or in any emphatic way (e.g.: I’m literally exhausted — I agree their example here contradicts the last Larousse example).

Here is a quote from Pensées (Thoughts) (1670) by Blaise Pascal:

Deux erreurs. 1. Prendre tout littéralement. 2. Prendre tout spirituellement.

Two mistakes. 1. Take everything literally. 2. Take everything spiritually.

As to why we’re using this word wrongly, the newspaper Le Figaro blames the anglicism “literally” that was translated as “littéralement” in TV shows such as How I Met your Mother. I wouldn’t take their word for granted.

I hope I was able to help. If not, my apologies!