Naturalization files are kept at the National Archives Centres, either in Paris for older records or in Fontainebleau for the more recent ones (after 1930).
There are several ways of acquiring French Nationality, but naturalizations by decree are publicly announced and printed in the official gazette of French Republic, either the "Bulletin des Lois" (1814-1961) or the "Journal Officiel" (also called for short J.O.) from 1924.
So, theoretically, if you know the date of the decree, you can check out the corresponding gazette at any Departmental Archives Center.
However, as this information is generally unknown to begin with, a serie of books listing all naturalizations were published : "Liste alphabétique des personnes ayant acquis ou perdu la nationalité française par décret" which cover the 1900/1979 time-period in several volumes. Those books are of course available at the National Archives (both centres) but I'm not sure if Departmental Archives have all the volumes, if any. Some genealogical associations or even private individuals have also some or all of them.
But more interestingly, one of the biggest French genealogical company compiled these data on several CD-roms: http://www.genealogie.com/v2/genealogie-boutique/rechercher....
They also offer to search their database on-line, though they only give you the naturalization year if you have no (paying) membership: http://www.genealogie.com/archives-historiques/9/Decorations...
(type in the surname)
No need to spend money for a one-time search however, it's easy to find people who have the CD and are kind enough to do the search for you, such as here: http://www.genealogie.com/v4/forums/recherches-genealogiques...
or here: http://www.geneanet.org/forum/index.php?topic=291325.0
From the books or the CD-rom, you'll learn these informations:
- name and first name(s)
- birth date and country/town
- decree date and reference
- from 1948, the file reference
Note that the file number/reference is different from the decree number AND needed to request a copy of the file at the National Archive Centre. Strangely enough, for the 1931/1948 period, the records are kept at Fontainebleau but they can't find the file number on the premises, they have to fill a request to the 'Sous-direction de l’accès à la nationalité française' near Nantes (Immigration Office), which delay the search for a while as there is a several weeks waiting list... but once they've got the file reference, you can access the file in the hour! ;)
Anyway, if you can't go yourself in Fontainebleau, there are several mutual-aid services and benevolents which will agree to do the search for you against a little fee (such as here: http://www.notrefamille.com/v4/forums/recherches-genealogiqu...
) or you can ask directly the Archives to photocopy the complete file (if its state allow it) and send a copy to you for a fixed tax (around 18€):
. Paris Centre:
60 rue des Francs-Bourgeois
. Fontainebleau Centre:
Centre des Archives Contemporaines
2 rue des Archives
I forgot to mention you can only consult more than 50 years old files because of privacy laws, but that should not be a problem in your case.
Hope that answer your question and let me know if you need more explanations. ;)