A look at the trilingual dictionary Dictionary of Commercial, Financial and Legal Terms (HERBST, ed. Spinger) shows us that indeed both account (-ing, -ancy) and bookkeeping are used to translate the French comptabilité.
- Le bureau de la comptabilité → Accounts department
- La comptabilité commerciale → commercial bookkeeping
- a "bookkeeper" and an "accountant" are both called comptable in French.
Wikipedia has a page Comptabilité in French that links to the page "Accounting or accountancy" in English.
The English page bookkeeping in Wikipedia has no French counterpart.
It is a fact though that tenue de compte (the exact French translation of "bookkeeping") exists but is hardly ever used outside the banking world and what a French person will read as "frais de tenue de comptes" will be listed as "bank account fees" on a bank statement written in English.
This could lead us to think that the difference between "accountancy" and "bookkepping" is a cultural one and if you look deeper into this we can see that the difference is not that obvious to the English speaking world and sometimes needs to be explained.
If we look at comptabilité in Termium Plus (The Government of Canada’s terminology and linguistic data bank) we can seen they distinguish between
Champ d'expertise recouvrant l'ensemble des compétences, responsabilités, recherches et activités comptables, y compris les principes, normes, méthodes et systèmes, envisagés tant du point de vue théorique que pratique. (translated as "accountancy" in English)
Système d'information permettant de rassembler et de communiquer des informations à caractère essentiellement financier, le plus souvent chiffrées en unités monétaires, concernant l'activité économique des entreprises et des organismes (translated as "accounting" in English)
- tenue des comptes
Travail qui consiste à classer et à enregistrer les opérations et les faits économiques se rapportant à une entité dans les comptes de celle-ci. (translated as bookkeeping in English) With the following note: On emploie parfois le terme «comptabilité» au sens de tenue de la comptabilité. (Sometimes the word "comptabilité" is used with the meaning of bookkeeping.
Pierre Labardin, a lecturer in management and Marc Nikitin, professor in management, wrote a paper about the history of the word comptabilité from a linguistic and historical perspective. We learn in this paper that the merging of the words "bookkeeping" and "accounting" is fairly recent in French history. In their abstract they write:
In the French language, the word comptabilité (accounting) has gradually replaced tenue des livres (bookkeeping) around the beginning of the 19th century. After that, adjectives were
progressively added (commercial accounting, industrial accounting, general accounting, auxiliary accounting, etc.), in keeping with the division of labour in newly created accounting departments.
The first part of the paper is called I. De la tenue des livres à la comptabilité (From bookkeeping to accountancy).