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.