Preparing the "after-PhD"
From October of your 3rd year of PhD, post-doc offers start arriving for the following year. If you want to continue in the research, you can check these websites that list post-doc offers:
Many offers go through the astro-jc mailing list. To register, follow the instructions (in french).
The doctoral school share post-doc offers on Twitter: @ED_AAIF
If you do not know the professional perspectives available to you at the end of the PhD in academic and/or industrial sectors, you can follow the doctoral course « Préparer l'après-thèse : les métiers et carrières après la thèse dans ou hors recherche publique » (in french) proposed by ED127. You can find doctoral courses about this subject in course catalog on ADUM website.
See the french page for the "qualifications" (required to get a permanent position at the University).