Ok thanks for all the valuable feedback. I think this text problem needs some clarification.
1. Yes. English is not my native language. I can write in French, German, Japanese... but not in English. This is a problem in this kind of game. Even more so when it's based on a pretty strong scenario.
2. That's why I had asked someone to do a editor job and avoid this kind of problem. A job that cost me some money (you can see my ad in the recruitment section). Exchanges with this person show that there is a misunderstanding in the expected result.
That's unfortunate. It seems like the proofreader in question probably had a different expectation of what the job entails.
If that's the english
after the improvements, it's likely that you're looking more for a (ghost)writer than an editor.
Proofreading primarily focuses on finding oversights in grammar, syntax, spelling & diction, who essentially sharpen what's already there to a point & remove the last flaws.
This type of ghostwriting requires the writer to basically go through every sentence and use them as source to rewrite the text. That's a ton of work more than proofreading, because you need to divine the intent in what's being sad, read the subtle clues that the original writer wants to give, capture the tone & pacing that's intended, etc.
One way in which you can make this easier for the person doing it is providing a scene outline. That's basically a brief summary & explanation of what the scene intends to convey and what they main focus point is. Otherwise writers will have to attempt to divine this from existing text which can easily go wrong.
3. I don't hide the fact that the poor quality of the texts in English disappoints me a lot. I will have to find a way to make changes in the existing content and in the texts that are already written in chapter 2.
That's not something to beat yourself up about. No one can just write text in a foreign language. It can take many years of professional practice to get good at it.
If you're still in contact with your current editor (if you're still working together), you may want to discuss how best to move forward & be sympathetic to the fact that the scope of your request probably exceeded what was expected as workload. But it's also quite clear that the current level of proofreading is not sufficient, so if the proofreader isn't interested in this - or doesn't believe they can manage that (even if the procedure is changed, e.g. through scene outlines) - you may have to find someone else.
The bad news is that it's probably not going to be cheap.
The best option would be someone who, as you say, is not only experienced in writing english, but also fluent in french - that would make it a lot easier for you to communicate your intentions.
Alternatively you look for a writer to collab with (cheaper, but it will be a permanent revenue cut and you'll have to live with their own interpretations) or to hire someone to ghostwrite the text for you (a lot more expensive and requires direct pay, since you're looking for a very high degree of experience in the writer, since they have to be able to read your intentions).