Joe wrote:
I recently bought a return ticket from France to French Indies, coded
"First Class", displayed "First Class" by QPX (ITA Software) pricing
system and sold with the A fare code ("discounted first class"

There are 3 different things/terminology:

***Fare BASIS:
a fare code, usually of a few characters ( such as QWNR14 ) but can also be
a single letter such as "Y" and, combined with cities of origin/destination
and travel date, specify not only a price, but also the fare rules, allowable
routings. It also specify that a reservation must be booked in a specific
booking code. *USUALLY*, the booking code required for that fare basis to
apply is the first letter of the fare basis. The fare basis will specify the
service class (coach, business, first)

***Booking class: a one letter code which identifies which inventory of seats
a reservation will draw upon.

So technically, you first make a reservation in a certain booking class. Then,
you find fares applicable to that booking class, price the ticket and then
issue ticket.

For research, you look at the fares you want, find out in which booking class
you need to find inventory where this fare is applicable, book it etc.

If you booked a first class fare, and the airline widthdrew first class
service, then they should refund the difference compared to a similar advance
purchace fare in coach vs first. However, there are fare rules that do
stipulate that travel may be in coach on segments where first class is not
offered. (considered a round the world package booked in first class but using
flights on an airline that has no first class. This is documented in the fare
rules for those RTW packages.

How come that fare codes do not exactly match cabin classes ?

They never did. The only standards were Y for coach, J for business class and
F for first. But there have been exceptions for first (P, and for Concorde R).

of the "A" fare code by the airline (A for "Alizee" instead of A for
"discounted first class" according to IATA rules seems to be
misleading software systems - and passengers !).

Not at all. Booking class letters, except for Y J and F mean absolutely
nothing and nothing should be drawn from them. One some airlines, A could be
used to define capacity in first class with on the other airline it could be
used to allocate capacity in coach for dicounted fares.

Similarly, except for fare basis that begin with Y J and F, you can't draw any
conclusions as to where you will be seated, althoug generally, if it isn't J
or F, you are in coach. You need to look at the full fare rules associated
with the fare basis for your segment to know exactly what applies to you.

This is one area where the dumbed down Web sites have done much harm because
their have artificially shielded customers from what really happens when you
book air travel, so customer never lear hwo things really work and things
don't go exactly well, there is no way to know what really happened.

To what extent is it permitted for an airline company to sell "first
class discounted" tickets to passengers that will eventually travel in
economy class or enhanced economy ?

If at the time you booked and had ticket issued, there was available capacity
in first class on the flight you requested, then it is permitted. Airlines
routinely adjust their schedules, substitude equiopment, cancel flights, or
redesign aircraft layouts to resize or eliminate first class/business class.