Write the whole thing in French. You are applying for a job where you will have to teach 192h per year in French. Committees arewary of hiring someone only to find out that they cannot do half of their duties because they don't speak the language. The department would need to scramble to find someone to replace the hired person for the courses they are assigned etc.
An application written in English will be viewed negatively and will hurt your chances. Unless you have an amazing track record, your name will probably not make it to the shortlist of interviewed people. And if it does, you will have to do your absolute best to convince the committee that you speak French adequately.
I was on hiring committee a couple of years ago. We got more than 80 applications. Only three were written in English and were rather eccentric (people who didn't even have a PhD in math, usually) and weren't shortlisted.
I'd also like(This answer used to dispute the idea thatcontain a link to an old version of the expectation thatregulation regarding applications need to be in French is only implicit. See Arrêté du 6 février 2023 relatif aux modalités générales des opérations de mutation, de détachement et de recrutement par concours des maîtres de conférences, des professeurs des universités et des chaires de professeurs juniors and especially Article 9:
Les documents administratifs rédigés en tout ou partie en langue étrangère sont accompagnés d'une traduction en langue française dont le candidat atteste la conformité sur l'honneur. La traduction de la présentation analytique est obligatoire et les travaux, ouvrages, articles et réalisations en langue étrangère doivent être accompagnés d'un résumé en langue française. A défaut, le dossier est déclaré irrecevable.
If you write your "Présentation Analytique" in English and do not provide a translation, you run- the new version does indeed state that the risk of the HR department of the university can simply reject your application for noncompliance. It won't even get in front oftranslating the committee"Présentation analytique" is optional.)
Six pages is fine for the research statement, you don't need much more than that. A typical opening gets dozens if not >100 applicants. Adequate summarization skills are appreciated.
The absence of a teaching section will be noted, sure. This is an application for a job where half the duties are teaching. Committee members will wonder if you just don't care about teaching and will slack off if hired. One page is probably enough though.