Bad image quality in Gaspar Noé films

I've found a potential source of the issue, mentioned in the Trivia section on IMDB

The entire film was shot on Super 16, telecined to high-definition video for color tweaking and editing, and then exported to Super 35. For many of the handheld shots, the director used the smallest existing 16mm camera, the Minima.

In essence, that's why - low resolution film stock, compared to a "normal" film shot on 35mm [or larger] stock, or even modern digital.

I'd imagine this was an artistic decision, though you can never discount budgetary reasons. Unless someone can find a better info source, from the director himself, we may never know for sure.

From WIkipedia - Irréversible

Irréversible has been associated with a series of films defined as the cinéma du corps ("cinema of the body"), which according to Palmer share affinities with certain avant-garde productions: an attenuated use of narrative, assaulting and often illegible cinematography, confrontational subject material, and a pervasive sense of social nihilism or despair. Irréversible has also been associated with the New French Extremity movement.

This would potentially indicate the visual aspect is entirely intentional.

It is the fault of the people who worked on the video. Yes it's shot on 16mm so it maybe it could never be as good as some videos but I believe that it could be improved if there was a budget for it.

First of all it looks like the video had too much digital noise reduction applied to it. Since it's 16mm the grain is going to be larger on the video than 35mm.

Also this most likely plays a minor role into the issue but note that the scanning process can also introduce noise. I don't own a professional telecine machine but I have a 35MM negative scanner (for stills not reels) and it actually introduces quite a lot of digital noise that doesn't exist on the negative in part because it uses too fast of an exposure. I'd expect that some telecine machines are better than others. This could arguably necessitate the need for more digital noise reduction.

Second of all I noticed posterization. This can happen when grading an 8-bit image. You need a higher bit depth so the final looks good depending on how much you are changing the colors. Note that I don't have any proof that this was the issue but it's one possible explanation.

Third of all it looks like the image is heavily compressed. I'm not sure if that's because the screenshot was saved as a JPEG or it that's from the video. If it's from the video, it would benefit from a higher bit rate encoding.

Four of all and this one is very debatable, the color grading itself doesn't look good. Maybe the colors could be tweaked so more people subjectively like it. I haven't seen any of these movies so I cannot comment on this too much. I'm only judging from the screenshot presented in the question.

I do not have enough reputation to comment but may I also suggest you post screenshots from the movie 1:1 (no up-scaling or down-scaling) in PNG format and provide more screenshots so we can get a more objective view of the movie.

For example if you have mpv installed run:

 mpv --screenshot-format=png movie_filename.ext