Joe wrote :

.................
I am talking for example French stamps which are issued in several
millions of each face value, but which are also in use in other
islands belonging to France, such as in Reunion island or Guadeloupe,
where they use a different cancel having the name of the island where
it has been used.

Will such French stamps having the cancel with the name of Reunion
island or Guadeloupe or other islands belonging to France be worth
more in used condition than those used in France? These islands are
called in French "DOT-TOM, Deparment Outremer - Territoire Outremer" I
think that it is tranlated into English as "Overseas
Departments-Overseas Territories"

Joe,

Yes it is a good translation ;-)
(Just a small typo : it is DOM instead of DOT for Département
d'Outre-Mer)

On the value of cancelled stamps from DOM-TOM, theoretically, you are
right.
But I am not aware of any special demand on modern French stamps nicely
cancelled in the DOM-TOM (i.e. with a readable place of cancel and a
date corresponding to the period of validity of the stamp).

In France, there are not so many collectors appreciating used stamps
(compared to the vast majority of people *demanding* for MNH only).
For those who collect used stamps, it is quite difficult to find the
stamps they are missing if they insist to get a stamp with a readable
date (from the period of validity).

Difficult even if (or because ?) the catalog value is much less than for
a MNH.

All this is valid for modern stamps.

Of course, for 19th century French stamps, it is a different story and
the used stamps from Guadeloupe, Martinique, Reunion, ... have a much
higher cat. value compared to their equivalents from France
"Métropolitaine" ( = Inland France ?)

HTH

--
All the best,
Pierre Courtiade