I the United Kingdom there is a very useful website (jobs.ac.uk) which allows researchers to search academic jobs, including postdoctoral positions, lecturer's posts, and so forth. I have been looking for similar search engines for other countries, in particular France, without much luck. If anybody with some experience of looking for academic research positions, fellowships and contracts in France could share their experience it would be great.
Permanent positions ("maître de conférences" and "professeur") almost all are listed on the website called Galaxie. The lists are available on this page. It's a bit empty because most applications are over for this year, but there is still the big spreadsheet with the (now outdated) info, to give you an idea.
(There are also some permanent positions called "PRAG" and "PRCE" listed there but they are unlikely to concern you – you would know if they did.)
Some special postdoc positions called "ATER" (attaché temporaire d'enseignement et de recherche) are also listed there, however be warned that 1. their salaries are low, even lower than a PhD student, 2. the teaching load is high, as much as a faculty member, 3. they are often "reserved" for PhD students who are on the brink of finishing but need an extra semester or two. You probably have to ask someone from the university to know if it is the case (I know people who got an ATER who were not PhD students just finishing, so it's certainly possible).
Galaxie is not very well organized and it is a bit hard to find information. In some fields, volunteers run some field-specific websites presenting the same information in more readable form, e.g. Opération Postes in mathematics. Ask your contacts in French universities to tell you if one exists for your field.
I am not aware of any centralized website for postdoc applications. I have personally never searched for a postdoc in France, but in my understanding, you have to subscribe to mailing lists, go to labs' websites, or just know people who are aware of openings, etc. Good luck. Some things to look out for: if something is called a "fondation" (foundation), they probably have some postdoc grants to offer. Similarly if you come across something called a "Labex" (for "laboratory of excellence", yes, it's a bit pompous), it's not an actual lab, it's a five year big grant with many postdoc grants attached.
I realized that I said something wrong above. Not all permanent positions are listed on Galaxie. Some "Grandes Écoles" ("Great schools"), which are not technically universities, still hire professors who teach and do research. More info on Wikipedia. For these positions, I don't think you can do better than going on their websites when it's application season. The procedure is also different from the centralized one, from what I understand.
PS: yes, all these websites are in French... You will find that being able to read and write administrative French (or having someone who can on call) is a vital skill.
tl;dr There is no such website, basically.
you can check this website;
you can find postdoc offers there, some of them are listed in English.