The short answer is that oriental is the adjective associated to the noun est. “Eastern X” and “X oriental(e)” are in straightforward correspondance.
In French, you can't just take a noun and use it as an adjective. You often need to add or change a suffix, and sometimes more than that. There is no adjective built directly on est¹.
It's very common for “...
As a french native speaker living in Suisse romande, I can confirm that suisse orientale is commonly understood and used to speak of the east part of Switzerland (St-Gallen, Graubünden,...).
Though most of time, the whole german part of Switzerland is seen as suisse allemande for the people in suisse romande. As I lived in Zurich, I noticed that the ...
Qui est situé à l'est : La côte orientale de la Corse.
l'Orient : Peuples orientaux.
Qui est propre à l'Orient, à sa culture,
ses traditions : Musique orientale.
Qui est digne de l'Orient, tel
qu'il est imaginé dans la ...
The adjective "oriental(e)" designates something situated to the east, the orient.
The adjective "occidental(e)" designates something situated to the west, the occident
Sure you could call it "Suisse de l'est", but using the appropriate adjective is more elegant and in this case is not really ambiguous. For example in French, middle-east is not called "...