There is a "technical" classification of wines, such as "vin de
table" (table wine) which are usually made of grapes from mixed
origins but include the sub-category "vin de pays" (regional wine),
which cannot be mixed.
There are also the "appellation d'origine contrôlée" (controlled
origin) AOC wines, or the "vins de qualité supérieure" (of superior
quality) VDQS wines, which are even more reglemented for origin,
content and method.
As for quality classification, there is no such generic rating
system, but specific ones for different regions of France, or even
for different types of wine in the same region, such as the
Saint-Émilion, Médoc, Sauternes, etc. separate classifications (but
not Pomerol), all of them Bordeaux wines.
These classifications are usually revised every few years.
For Saint-Émilion for instance, the highest classification is
"grand cru classé A", then "B", then just "grand cru classé" with
no letter.
For Sauternes, the highest is "grand premier cru", "premier
cru", "deuxième cru".
Burgundy wines have "grand cru" then "premier cru".